text:
\section{Kan Extensions and 2-categories}
To express the main results we need to work with the notions of universality and Kan extensions. Recall that, given a functor $R : \C \to \D$, an object $A \in \ob\D$ has an $R$-universal arrow with the base object $B \in \ob\C$,  iff
\begin{eqnarray}
\hom_{\D}(A,-)\po R \cong \hom_{\C}(B,-).\label{uni}
\end{eqnarray}
\begin{rem}\label{colim}
For instance, if $\D$ is a small category and $\Cons : \C \to \C^{\D}$ sends objects and morphisms on constant functors and constant transformations, respectively, then, given a diagram $D: \D \to \C$, its colimit (if any) is the base object of a $\Cons$-universal arrow over $D$.
\end{rem}
\subsubsection*{Kan Extensions and Codensity Monds}
Let us recall the concept of Kan extensions briefly. For the main sources, see \citep{mac,bor1}.

Let $\A$, $\B$ and $\C$ be categories and $S: \A \to \B$ , $U:\A \to \C$ be functors. A {\em right Kan extension of $S$ along $U$}
is a pair $\Ran_U S=(T,e)$ consisting of a functor $T: \C \to \B$ and a natural transformation $e:TU \to S$ satisfying the following universal property (Kan universality):\\
given a functor $T': \C \to \B$ and a transformation $e':T'U \to S$, then there is a unique transformation $t:T' \to T$ such that $e'=e \po tS$. Then we write $T=\ran_U S$.

$\Ran_U S$ can be defined equivalently as a $[-\po U]$-couniversal arrow $(T,e)$ over a functor $S: \A \to \B$, here $[-\po U]$ is the abbreviation of the corresponding functor $\CAT(U,\D): \CAT(\C,\D) \to \CAT(\A,\D)$. Hence the right Kan extension can be given by an isomorphism
\begin{eqnarray}
\hom_{\End \C}(-,S) \po [-\po U] &\cong& \hom_{\End \C}(-,\ran_U S). \label{homhom}\label{kan2}
\end{eqnarray}

The right Kan extension is said to be {\em pointwise} if it can be obtained by the following procedure:

Given an object $A$ in $\C$, then $Q_A:A \downarrow U \to \A$ will denote the forgetful functor for the comma category. Consider the functors $S \po Q_A$ for every $A \in \ob\C$. If each of these functors, seen as a large diagram, has a limit $T_A \in \ob\B$, then the assignment $A \mapsto T_A$ yields a functor $T:\C \to \B$ and there is a natural transformation $e:T\po U \to S$ such that $(T,e)=\Ran_U S$.

Suppose $\Ran_U S=(T,e)$ exists. Then is pointwise iff it is preserved by $\hom(C,-)$ for every object $C$ in $\C$.

The relation between Kan extensions and adjunction is captured in the equivalence of the following statements:
\begin{enumerate}
\item \label{adran1}$F$ has a left adjoint.
\item \label{adran2}$\Ran_F \Id_{\A}$ exists and $F$ preserves it.
\item \label{adran3} $\Ran_F \Id_{\A}$ exists and $F$ preserves all right Kan extensions with the values in $\A $.
\end{enumerate}

Since, on a category with copowers, every hom-functor is right adjoint, the implication $(\ref{adran1}) \imp (\ref{adran3})$, together with the previous statement, yields an important fact:
A right Kan extension with the values in a category with copowers is pointwise.

Given a diagram $D:\D \to \A$ and a terminal functor $T:\D \to {\bf 1}$, then $\Ran_T D=(C_L,\lambda)$ consists of the constant functor $C_L:{\bf 1} \to \A$
with $L$ being the limit object of $D$ and $\lambda=\{\lambda_d:L \to Dd|,d \in \ob\D\}$ being the limiting cone. Dually, colimits can be obtained by left Kan extensions.

Given a functor $U:\A \to \C$ with the right Kan extension $\Ran_U U=(M,e)$, then there exists a monad $\MM=(M,\eta,\mu)$ on $\C$ with the transformations $\eta:\Id_{\C} \to M$ and $\mu:M^2 \to M$ induced, via Kan universality, by $\id_U:U \to U$ and $e \po Me:M^2 U\to U$, respectively.

The above monad $\MM=(M,\eta,\mu)$ together with the transformation $e$ is called {\em codensity monad} for $U$. If the corresponding right Kan extension is
pointwise, we say $(\MM,e)$ is a {\em pointwise codensity monad}. If $(\A,U)$ is the concrete category, we say $\MM$ is its codensity monad.

\subsubsection*{Kan Extensions in 2-categories}\label{2-cat}
Given a 2-category $\AQ$, then, for each pair of its 0-cells $A$, $B$ the {\em category} of 1-cells $A \to B$ as objects and 2-cells as morphisms will be denoted by $\Hom(A,B)$ while we keep the notation of {\em hom-sets} (of 1-cells or 2-cells) denoted by "$\hom$".
For a more detailed overview of a 2-category theory, see \citep{street,lackstr,lack}.

The concept of Kan extensions is well established in every 2-category -- just think of every 0-cell, 1-cell, 2-cell as of a category, a functor, a natural transformation, respectively.

We are going to prove a property on Kan extensions in a 2-category which might be well-known but no source known to the author seems to contain it. It involves the notion of 2-couniversality (a weaker condition to an adjunction between 2-categories).

\begin{de}({\em 2-couniversality})
Given two 2-categories $\AQ$, $\BQ$, a 2-functor $L: \AQ \to \BQ$ and an object $B$ of $\BQ$, we say an object $Q$ of $\AQ$ is {\em $L$-2-couniversal} (briefly $L$-couniversal) over $B$ if there exists a 2-natural isomorphism between 2-functors $$K:\Hom_{\BQ}(-,B) \po L \to \Hom_{\AQ}(-,Q).$$
\end{de}
From now on, let the above instance of 2-couniversality take place.
\begin{lm}
Given objects $A$, $C$ of $\AQ$, morphisms $g:A \to C$ and $h:LC \to B$, then
$$K_A(h \po Lg)=K_Ch \po g.$$
\end{lm}
\begin{proo}
Since $K$ is a 2-natural transformation, we have $$K_A(h\po Lg)=K_A \po \Hom(Lg,B)(h)=\Hom(g,Q) \po K_C(h)=K_Ch \po g.$$
\end{proo}

\begin{rem}
Given objects $A$, $C$ of $\AQ$, morphisms $f:LA \to B$, $g:A \to C$ and $h:LC \to B$, then the 2-cell-function of $K_A$ defines an isomorphism
$\hom(h \po Lg,f) \cong \hom(K_C(h) \po g,K_A(f)) $
and due to naturality of $K$ we get a natural isomorphism
\begin{eqnarray}
\hom(-,f)\po [-\po Lg] &\cong& \hom(-,K_A f)\po [-\po g] \po K_C. \label{ka}
\end{eqnarray}

\end{rem}

\begin{theo}\label{kanuni}
Let $\AQ$ and $\BQ$ be 2-categories, $L:\AQ \to \BQ$ be a 2-functor and $B$ an object in $\BQ$ with an $L$-couniversal object $Q \in \ob\BQ$. Given objects $A, C$ in $\AQ$ and morphisms $f:LA \to B$, $g:A \to C$, then
$$\Ran_{g}(K_A f) \cong K_C \Ran_{Lg} f$$
whenever $\Ran_{Lg} f$ exists.
\end{theo}
\begin{proo}
Let $\ran_{Lg} f$ exist, then by application of (\ref{kan2}) and of the previous remark
we have:
$$
\barr
\hom(-,K_A f)\po [-\po g] \po K_C &\stackrel{(\ref{ka})}{\cong}&  \hom(-,f)\po [-\po Lg] \\
&\stackrel{(\ref{kan2})}{\cong}&  \hom(-,\ran_{Lg}f)\\
&\stackrel{(\ref{ka})}{\cong}&  \hom(-,K_C \ran_{Lg}f) \po K_C
\end{array}
$$
and since $K_C$ is an isomorphism, we get $$\hom(-,K_A f)\po [-\po g] \cong \hom(-,K_A \ran_{Lg}f).$$ Hence $K_A \ran_{Lg}f \cong \ran_{g}(K_A f)$ which can be extended analogously on natural transformations to get the required equality.
\end{proo}

\subsubsection*{Kan Extensions of Cones}
Our interest will be in limits of concrete categories. Therefore, it will be suitable to study Kan extensions of cones. These will be defined using the language of 2-categories.

Consider a 2-category $\AQ$. If $\D$ is a small category, then the category $\AQ^{\D}$ of functors $\D \to \AQ$ can be treated again as a 2-category with the cell-structure defined pointwise. Now the objects of $\AQ^{\D}$ can be seen as $\D$-domained diagrams.

We define a 2-functor $\Const: \AQ \to \AQ^{\D}$ as depicted bellow (with 0-cells $\A$, $\B$, 1-cells $F$, $G$ and a 2-cell $\alpha$):

$$ \begin{array}{ccc}
\xymatrix{
\A \rrtwocell_G^F{_\;\:\alpha} &&
\B
} & \mapsto &
\xymatrix{
C_{\A} \rrtwocell_{c_{G}}^{c_{F}}{_\quad{\rm c}_{\alpha}} &&
C_{\B}
}
\end{array}
$$
where $C_{\A}$ denotes an $\A$-constant functor, $c_F$ is a $F$-constant natural transformation and ${\rm c}_{\alpha}$ stands for an $\alpha$-constant modification of natural transformations.

Given a category $\A$, then a 1-cell $\Const\A \to D$ is a $D$-compatible cone and a 2-cell between such cones is a $\D$-indexed collection of natural transformations.

By analogy to the Remark \ref{colim}, we can define cone limits in 2-categories using the notion of 2-couniversality.

\begin{de}
Given a 2-category $\AQ$, we say a diagram $D:\D \to \AQ$ has a limit $l \in \ob\AQ$ if $l$ is a $\Const$-2-couniversal object over $D$.
\end{de}

The concept holds obviously even for large 2-categorical structures. Consider a 2-metacategory $\CA2$ with the usual cell-structure and a category $\D$ (the smallness condition will not be necessary).
Now, given a diagram $D:\D \to \CAT$, functor $G:\A \to \B$ and a cone $F:\Const\A \to D$, a {\em Kan extension of the cone $F$ along the functor $G$} is the Kan extension of $F$ along $\Const G$ in the 2-category $\CA2^{\D}$.
$$\xymatrix{\Const\A \ar[rr]^{F}\ar[drr]^{\Const G} && D\\ && \Const\B \ar[u]_{\ran_{\Const G}F}}$$
Now the Theorem \ref{kanuni} has the following consequence:
\begin{lm}\label{konlim}
Let $D:\D \to \CA2$ be a diagram and $\L$ be its limit and $\A$ be a category. Given a cone $F:\Const\A \to D$ and a functor $G:\A \to \B$, then if $\ran_{\Const G} F$ exists, then
$$\ran_{G} \widetilde{F} \cong \widetilde{\ran_{\Const G} F}$$
where $\widetilde{\:}$ stands for the factorization over the limit cone.
\end{lm}
\begin{proo}
Since $\L$ is the limit of $D:\D \to \CA2$, it is a $\Const$-2-couniversal object over $D$, hence the statement follows directly form the Theorem \ref{kanuni}.
\end{proo}

We say $\Ran_{\Const G}F$ is {\em componentwise} Kan extension if it is a collection of the right Kan extensions, i.e., $$(\forall d\in \ob\D)\: (\Ran_{\Const G}F)_d= \Ran_{G} F_d.$$
\begin{rem}\label{compkancone}
Under the above assumptions, it is easy to show the equivalence of the following:
\begin{enumerate}
\item A componentwise right Kan extension of the cone $F$ along $G$ exists.
\item For every object $d \in \ob\D$, a $\Ran_G D_d$ exists and these Kan extensions are preserved by all composable functors of the form $D\phi$, $\phi \in \mor\D$.
\end{enumerate}
\end{rem}
Since the usual limits can be obtained as right Kan extensions of the diagram along the terminal functor, we may consider the following analogue.
\begin{rem}
Let there be a diagram $D:\D \to \CAT$ with the limit $\L$ and the limiting cone $L$ and a diagram $G:\G \to \L$ and the terminal functor $T:\G \to \1$. Coherently with the usual concept of Kan extensions, the $\Ran_{\Const T} (L \po \Const G)$ will be called a {\em limit of the cone diagram $L \po \Const G$}. In fact, it is a choice of the limit (object and the limiting cone) of each $L_d \po G$, such that they are preserved by functors $D\phi:Dd \to De$ for $\phi:d\to e$ in $\mor\D$.
If $D$ has a limit, any cone can be seen as a cone diagram since it factorizes uniquely over the limiting cone.
\end{rem}

As a direct consequence of the Lemma \ref{konlim} we can show that Kan extensions are created by limiting cones of categories.
\begin{theo}\label{limkancone}{\rm (Limiting cones create Kan extensions.)}
Let there be a diagram $D:\D \to \CAT$ with the limit $\L$ and the limiting cone $L=\{L_d:\L \to Dd|,d \in \ob\D\}$. Let there be categories $\A$, $\B$ and functors $V:\A \to \B$, $S:\A \to \L$. Consider the induced cone $K=L \po \Const S$. If $\Ran_{\Const V} K$ exists, then $\Ran_V S$ exists as well and $L \po \Const\Ran_V S \cong \Ran_{\Const V} K$.
\end{theo}
\begin{rem}\label{leftkancone}
By duality of categories $\A,\B,\L,D_d$ in the theorem, one gets that limiting cones create left Kan extensions as well.
\end{rem}
\begin{lm}\label{limkan}
Let there be a diagram $D:\D \to \CAT$ with the limit $\L$ and the limiting cone $L$ and $G:\G \to \L$ be a diagram in $\L$. If the limit of the cone diagram $L \po \Const G$ exists, the limit of $G$ exists as well and $L$ preserves it.
\end{lm}
\begin{proo}
Observe that, for every pair of functors $\xymatrix{\bullet & \bullet \ar[l]_{Q} \ar[r]^{P}& \bullet}$ there is an isomorphism $\Ran_{\Const Q}\Const P \cong \Const \Ran_Q P$ and that the limit of the constant functor is the target object itself.
Then, since $\widetilde{H}=L \po \Const H$ for every functor $H:\X \to \L$,
we have
$$\barr
\lim(L \po \Const G) &=&\ran_{\Const T}(L \po \Const G) =\ran_{\Const T}(\widetilde{G})\\
&\cong& \widetilde{\ran_T G}\\
&=&L \po \Const \ran_T G \cong L \po \ran_{\Const T} \Const G\\
&=&L \po \lim \Const G = L \po \Const \lim G.
\earr
$$
\end{proo}
\section{Concrete Categories and Algebras}\label{limcc}
The reader is expected to be familiar with the concept of concreteness, functor algebras and monadicity. To clarify the notation, given a category $\C$, a $\C$-concrete category with the forgetful functor $U:\D \to \C$ will be denoted by $(\D,U)$ or just by $\D$ if we do not need to emphasize the name of the forgetful functor. If the choice of this functor is obvious, the forgetful functor is usually denoted by $U_{\D}$. If concrete categories $\A$ and $\B$ are concretely isomorphic, we write $\A \cong_{\C} \B$.

Recall from \citep{Rac}, a $\C$-concrete category $(\A,U)$ is said to be a {\em Beck category} if $U$ creates all limits and coequalizers of $U$-absolute pairs. Beck categories include all categories of algebras and of algebra-like objects.

Given a functor $F: \C \to \C$, the category of $F$-algebras will be denoted by $\Alg F$. A category isomorphic to $\Alg F$, for some functor $F:\C \to \C$, will be called {\em f-algebraic}. It can be shown that every f-algebraic category is Beck.

\begin{rem}\label{alglim}
Given a category $\C$, the metaclass of $\C$-concrete categories and $\C$-concrete functors will be denoted by $\Con \C$ and referred to as {\em category of $\C$-concrete categories}.
The operator $\Alg$ may be considered contravariant functor $\End \C \to \Con \C$  defined on the category of endofunctors on $\C$. It assigns, to a natural transformation $\phi:G \to F$, the concrete functor $\Alg\phi:\Alg F \to \Alg G$ given by equality $(\Alg\phi)(A,\alpha)=(A,\alpha \po \phi_A)$.
\end{rem}

To revise the notion of monadicity, recall that, given a monad $\MM= (M, \eta, \mu)$ on $\C$, a {\em category $\MM\alg$ of
$\MM$-algebras} (also called Eilenberg-Moore category) is a full subcategory of $\Alg M$ consisting of all $M$-algebras $(A,\alpha)$ satisfying the {\em
Eilenberg-Moore identities} $\alpha \po \eta_A=\id_A$,
$\alpha \po M\alpha =\alpha \po \mu_A$.
A category concretely isomorphic to $\MM\alg$ for some monad $\MM$ is called {\em monadic}. The Eilenberg-Moore category $\MM\alg$ has free objects and the corresponding free functor $W_{\MM\alg}$ assigns, to an object $A$, the algebra $(M A,\mu_A)$.
It yields the adjunction $W_{\MM\alg} \dashv U_{\MM\alg}$ with the associated monad equal to $\MM$, which is also the codensity monad for $U_{\MM\alg}$. For more detailed treatment of monadic categories see \citep{mac,AHS,bor1,bor2}.

The following well known theorem characterizes all monadic categories:
\begin{theo}{\rm (Beck's theorem)}\\
Let $\A$ be a concrete category. Then
\begin{center}
$\A$ is monadic $\iff$ $\A$ is a Beck category with free objects.
\end{center}
\end{theo}

\subsection{Limits of Concrete Categories}

In this section we will work with diagrams of concrete categories over a base category $\C$.
By a (small) {\em diagram $D$ of concrete categories} we mean a functor $D: \D \to \Con \C$ from some (small) category $\D$.

Since, for each concrete category $(\A,U)$, $U$ is a faithful functor $\A \to \C$, we may consider $\Con \C$ a subcategory of the "slice-category" $\CAT / \C$ containing those pairs $(\A,U)$ where $U$ is faithful.

\begin{lm}
$\Con \C$ is closed under limits in $\CAT / \C$.
\end{lm}
\begin{proo}
The limits of concrete categories are computed as limits in a slice category -- the product is a wide pullback of the diagram connected by forgetful functors and the equalizer is an equalizer of the "non-concrete part" of the pair. The forgetful functor $U_{\L}$ for the limit category $\L$ can be obtained by composition of any forgetful functor of a category in a diagram with the corresponding limit-cone component. All we need to show is the faithfulness of this forgetful functor.

Let a pair $\xymatrix{\bullet \ar@<+0.5ex>[r]\ar@<-0.5ex>[r] &\bullet}$ in $\L$ be collapsed by $U_{\L}$ into an arrow. Then, due to factorization of $U_{\L}$ over faithful functors for each component of the corresponding diagram we have a cone with the domain ${\bf 2}$. Hence, there is a unique functor ${\bf 2} \to \L$ which makes the original arrows equal.
\end{proo}

\begin{rem}\label{conpro}
Since $\CAT$ is complete w.r.t. small diagrams, so is $\CAT / \C$, hence $\Con \C$ is complete as well. In particular, there exist products in $\Con \C$. Given two concrete categories $\A$, $\B$, their concrete product will be denoted by $\A \times_{\C} \B$, and can be obtained as a fibre-wise product, i.e., $$U_{\A \times_{\C} \B}^{-1} (A)=U_{\A}^{-1} (A) \times U_{\B}^{-1}(A).$$ The product of an infinite number of concrete categories can be described analogously.
The terminal object, i.e., the product over the empty index set, is the base category itself and the terminal morphisms are forgetful functors.
\end{rem}
It is easy to check that the functor $\Alg$ turns colimits into limits, i.e., e.g., $$\Alg(F+G) \cong \Alg F \times_{\C} \Alg G.$$
\begin{rem}\label{classint}
It is easy to see, that, moreover, the intersection of a large collection of subcategories exists.
Clearly, it contains all objects and morphisms, which occur in all categories of collection.
\end{rem}

\begin{lm}\label{limbeck}
Let $(\L,U)$ be the concrete limit of a diagram $D:\D \to \Con \C$. Let $G:\G \to \L$ be a diagram in $\L$ such that the forgetful functor $U_d$ creates the limit of $L_d \po G$ for each $d \in \ob\D$. Then $U$ creates the limit of $G$.

Dually, if the forgetful functors create the corresponding colimits, then so does $U$.
\end{lm}
\begin{proo}
To see this property for limits, let $U \po C_G$ have a limit. Since $U=U_d \po L_d$ for every object $d \in \D$ and the functors $U_d$ create the limit of $L_d \po G$, we have the limit of each $L_d \po G$. Moreover, the functors $L_d$ create the limiting cones, i.e., there is always a unique cone $\lambda^d_q$ of $L_d G$ for each $d$. Hence, for every morphism $\phi:d \to e$ in $\D$, we have $D\phi \lambda^d_q=\lambda^e_q$. Therefore there is a $D$-compatible cone $M$ with the domain $\1$ such that $M_d(0)=\lim L_d G$. Hence $M$ is a limit of the cone diagram $L \po C_G$. Due to Lemma \ref{limkan} it creates the limit of $G$, i.e., the limit of $G$ exists and is preserved by every $L_d$.

The property for colimits can be reached using the dual property (Remark \ref{leftkancone}).
\end{proo}

Immediately, we get the consequence.
\begin{coro}\label{limbeck}
A (possibly large) concrete limit of Beck categories is Beck.
\end{coro}
\subsection{Algebras for a Concrete Diagram}
\begin{de}
A limit, denoted by $\Alg D$, of a (possibly large) diagram $D: \D \to \Con \C$ with every object mapped on an f-algebraic category, will be called an {\em l-algebraic category}. If the category $\D$ has a weakly initial object, we say $\Alg D$ is {\em homogenous}.
\end{de}
\begin{rem}
Let $D :\D \to \End \:\C$ be a diagram with $D(x)=\Alg F_x$, where $F_x:\C \to \C$ is a functor for every object $x \in \D$.
The objects of category $\Alg D$ may be seen as {\em algebras for the diagram $D$}, i.e., the collections of
$\C$-morphisms $\{\alpha_x:F_xA \to A|x \in \D\}$ satisfying, for each $f:x \to y$ in $\D$, the $D$-compatibility condition $D(f)(A,\alpha_x)=(A,\alpha_y)$. The morphisms in $\Alg D$ are the morphisms of algebras for each
$x$, i.e., $\phi:(A,\alpha)\to (B, \beta)$ is a morphism if $\phi \circ \alpha_x = \beta_x \circ
F_x(\phi)$ for every $x \in \ob\D$.
\end{rem}
An analogous approach to the algebras for a {\em diagram of monads} was studied by Kelly in \citep{Kelly}.

The concrete product $\Alg F \times_{\C} \Alg G$ for some endofunctors $F, G$ on $\C$ is an example of l-algebraic category. Its objects are $\C$-objects with two structure arrows -- for both $F$ and $G$. However, if $\C$ has coproducts, then the category $\Alg F \times_{\C} \Alg G$ is isomorphic to $\Alg (F + G)$. Generally, if $\C$ is cocomplete and the diagram in the definition maps all morphisms on "f-algebraic functors", i.e., those concrete functors which are $\Alg$-images of natural transformations, then the obtained category is an f-algebraic category. Therefore we will focus especially on the diagrams which do not factorize over functor $\Alg$.

Here we show the basic property of each l-algebraic category.

\begin{lm}\label{lbeck}
Every l-algebraic category is Beck.
\end{lm}
\begin{proo}
The statement is a direct consequence of property of f-algebraic categories and Lemma \ref{limbeck}.
\end{proo}

In Example \ref{proti} we show a Beck category which is not l-algebraic. Hence, the above implication cannot be reversed.

In \citep{pd}, the author shows that if $\C$ is cocomplete, all varieties in sense of \citep{AP} and all algebraic categories in sense of \citep{Rac} are l-algebraic.
\subsection{Polymeric Varieties}\label{polysect}
Another important family of concrete categories was introduced in \citep{p1}. It was shown that it includes many natural examples. To recall the definition, we need the notion of {\em polymer}.
\begin{de}
Let $(A,\alpha)$ be an $F $-algebra. Given $n \in \omega$, a {\em $n$-polymer} of an algebra $(A,\alpha)$
is the morphism $\alpha^{(n)}:F^n(A) \to A$ in $\C$ defined recursively:
$$\alpha^{(0)}=\id_A, \alpha^{(n+1)}=\alpha \circ F \alpha^{(n)}.$$
\end{de}
\begin{rem}\label{polyfun}
The assignment $(A,\alpha) \mapsto (A,\alpha^{(n)})$ clearly defines a functor $P_n:\Alg F \to \Alg F^{n}$.
\end{rem}
Now we have a sequence of functors $F^n$ together with functors between the categories of their algebras. This leads us to the definition:
\begin{de}\label{polymeric}
Let $n \in \omega$ and $G $ be an endofunctor on $\C$. A natural transformation $\phi:G  \to F^n$ is called
{\em $n$-ary polymeric $G$-term} in
category of $F$-algebras. A pair $(\phi,\psi)_p$ of polymeric $G$-terms of arities $m$,$n$,
respectively, is called {\em polymeric identity} of {\em
arity-pair} $(m,n)$ with {\em domain} $G$.
Moreover, for an $F$-algebra $(A, \alpha)$, we define $$(A, \alpha)\models (\phi,\psi)_p \quad
\stackrel{def}{\iff} \quad \alpha^{(m)} \circ \phi_A = \alpha^{(n)} \circ \psi_A,$$ and we say that the $F$-algebra $(A, \alpha)$ {\em satisfies} the
polymeric $G$-identity $(\phi,\psi)_p$.

For a class $\I$ of polymeric identities we define a {\em polymeric variety of $F$-algebras} as the class of all algebras
satisfying all $(\phi,\psi)_p \in \I$. The corresponding full subcategory of $\Alg F$ is denoted
by $\Alg (F,\I)$. If $\I$ is a singleton, we say that $\Alg (F,\I)$ is {\em single-induced}.
A category concretely isomorphic to $\Alg (F,\I)$ for some $F$ and $\I$ will be called {\em polymeric}.
\end{de}
\begin{lm}
Every polymeric category is homogenous l-algebraic category.
\end{lm}
\begin{proo}
It is easy to see that a single-induced polymeric variety $\Alg (F,(\phi,\psi)_p)$, where $(\phi,\psi)_p$ is $(m,n)$-ary polymeric $G$-identity, is an equalizer of the pair of concrete functors obtained by the following compositions:
$$\xymatrix{&\Alg F^m \ar[dr]^{\Alg \phi}&\\
\Alg F \ar[ur]^{P_m}\ar[dr]^{P_n} &&\Alg G\\
&\Alg F^n. \ar[ur]^{\Alg \psi}&\\
}$$
A polymeric variety induced by a class of polymeric identities is the intersection of polymeric varieties induced by single polymeric identities, hence a homogenous l-algebraic category.
\end{proo}

The following lemma shows the presentation of monadic categories by polymeric identities.
\begin{lm}\label{monad}
\label{poly-monad}
Every monadic category is l-algebraic.
\end{lm}
\begin{proo}
Given a monad $\MM=(M ,\eta,\mu)$, the Eilenberg-Moore category $\MM\alg$ is a
polymeric variety of $M $-algebras induced by polymeric identities $(\eta, \id_{\Id})_p,
(\id_{\MM^2},\mu)_p$ of domains $\Id$, $\MM^2$, respectively, and arity-pairs $(1,0), (2,1)$,
respectively.
$$\xymatrix{
M^1&\Id \ar[l]_{\eta} \ar[r]^{\id}& M^0,
}\quad \xymatrix{
M^2&M^2 \ar[l]_{\id_{M^2}} \ar[r]^{\mu} &M^1.} $$
Therefore $\MM\alg$ is a polymeric category, hence it is l-algebraic.
\end{proo}
\section{Concreteness and Universality}
In order to solve some problems involving categories of algebras on category $\C$ such
as existence of free objects, it might be useful to know their properties on the level of
objects of category $\Con \C$. Their status can be expressed in terms of properties of contravariant functor $\Alg$.
To simplify the proofs, we express the concept of universality in the language of Kan extensions and codensity monads. The main results characterize free-objects existence in l-algebraic categories and all Beck categories and provide another characterization of monadic categories.

The author acknowledges the advice from H. E. Porst, J. Rosick\'{y} and J. Velebil concerning the connection of universality and the concept of Kan extensions.

All the topic in this chapter deals with the category $\C$, generally without any additional assumptions.
\subsection{$\Alg$-universality and Kan Extensions}
\begin{rem}\label{transalg}
Let $F$ be an endofunctor on $\C$, $U_F:\Alg F \to \C$ be the forgetful functor and $\A$ be a category. Then each functor $H:\A \to \Alg F$ can be seen as $H=(K,\kappa)$ where $K=U_F \po H: \A \to \C$ and $\kappa:FK \to K$ is a natural transformation such that $HA=(KA,\kappa_A)$ for every object $A$ in $\A$. Moreover, if $(\A,U_{\A})$ is a $\C$-concrete category and $H$ is concrete, then $K=U_{\A}$.
This property can be easily expressed in terms of isomorphism between two (illegitimate) contravariant functors
\begin{eqnarray}
\hom_{\Con \C}(\A,-)\po \Alg &\cong& \hom_{\End \C}(-,U_{\A}) \po [-\po U_{\A}], \label{funhom1}
\end{eqnarray}
where $[-\po U_{\A}]=\hom_{\CAT}(U_{\A},\C)$ is given by the assignment $F \mapsto F \po U_{\A}$ (see the introduction to Kan extensons).
\end{rem}
We will apply the concept of universal arrows on the contravariant functor $\Alg: \End \C \to \Con \C$ as follows:\\
Given a $\C$-concrete category $\A$ and a $\C$-endofunctor $F$ with a concrete functor $H:\A \to \Alg F$, then $(F,H)$ is an $\Alg$-universal arrow for $\A$ iff for every $\C$-endofunctor $G$ with a concrete functor $J: \A \to \Alg G$ there exists a unique transformation $\widetilde{J}:G \to F$ such that $J= \Alg \widetilde{J} \po H$. This can be expressed by the isomorphism
\begin{eqnarray}
\hom_{\Con \C}(\A,-) \po \Alg  &\cong& \hom_{\End \C}(-,F). \label{funhom2}
\end{eqnarray}
The following observation is due to J. Rosick\'{y}:
\begin{lm}
Let $\A$ be a concrete category. Then
\begin{center}
$\A$ has an $\Alg$-universal arrow $\iff$ $\A$ has a codensity monad.
\end{center}
\end{lm}
\begin{proo}
Since the existence of a codensity monad is just a different way of saying that $\Ran_{U_{\A}} U_{\A}$ exists, we need to show that $\Alg$-universal arrow exists for $\A$ iff $\Ran_{U_{\A}} U_{\A}$ does. But the natural isomorphisms
(\ref{funhom1}) and (\ref{funhom2}) together with (\ref{homhom}) yield exactly what we need: a functor $F$ is a base of an $\Alg$-universal arrow for $\A$ iff $F=\ran_{U_{\A}} U_{\A}$ since
$$\hom(-,F)\stackrel{(\ref{funhom2})}{\cong}  \hom_{\Con \C}(\A,-) \po \Alg \stackrel{(\ref{funhom1})}{\cong} $$
$$\stackrel{(\ref{funhom1})}{\cong}\hom_{\End \C}(-,U_{\A}) \po \hom_{\CAT}(U_{\A},\C)
\stackrel{(\ref{homhom})}{\cong} \hom(-,F)$$
\end{proo}

This fact enables us to investigate the universality in terms of Kan extensions and codensity monads. In the following sections, we will use this language to characterize the free-objects existence for two significant families of concrete categories.
\subsection{Beck Categories with Codensity Monad}
\subsubsection{Categories with Pointwise Codensity Monad}
\begin{lm}
Let $U:\A \to \C$ be a functor which creates all limits and has a pointwise codensity monad. Then $U$ has a left adjoint.
\end{lm}
\begin{proo}
Let $(M,\eta)$ be the pointwise codensity monad for $U$. Then, for every $A \in \C$, $MA=\lim(U\po Q_A)$ where $Q$ is the projection functor $A\downarrow U \to \A$. Since $U$ creates the limits, there exists an object $L(A)=\lim Q_A$ in $\A$ such that $\lim(U\po Q_A)=U\po \lim Q_A$. Moreover, the whole limiting cone can be lifted to $\A$, i.e., for every morphism $f:A \to UB$ there is a unique morphism $\widetilde{f}:L(A) \to B$ such that $U\widetilde{f}$ is $\langle f \rangle$, i.e., the $f$-labeled component of the limiting cone for $U \po Q_A$. This implies the equality $f=U\widetilde{f} \po \eta_A$ for every $f$. Hence $\eta_A:A \to MA =UL(A)$ is the $U$-universal arrow for $A$. Therefore the assignment $A \mapsto L(A)$ can be extended to a functor $L:\C \to \A$, which is left adjoint to $U$.
\end{proo}

As a direct consequence we have the following.
\begin{coro}
Every Beck category with a pointwise codensity monad is monadic.
\end{coro}
This, in fact, implies a stronger version of Beck's theorem:
\begin{theo}
Let $\A$ be a concrete category. Then
\begin{center}
$\A$ is monadic $\iff$ $\A$ is a Beck category with a pointwise codensity monad.
\end{center}
\end{theo}
We emphasize that if the category has colimits, then each codensity monad is pointwise.
 Hence, in case such a case, for every Beck category, the existence of free objects is fully determined by the existence of a codensity monad.
 Particularly in case of varieties, there is another description of free objects derived in \citep{p}.
\subsubsection{L-algebraic Categories with Codensity Monad}
In the text bellow we show a seemingly weaker result, that every l-algebraic category with a codensity monad has free objects. However, this framework is independent of pointwiseness of a given codensity monad and cannot be derived from the above theorem, as shown at the end of this chapter.
\begin{lm}\label{ranconc}
Let $(\A,U)$ be a $\C$-concrete category with the right Kan extension of $U$ along itself. Then for every $\C$-endofunctor $F$ and a concrete functor $J:\A \to \Alg F$ there exists $\Ran_U J =(V,e)$. This Kan extension is preserved by
\begin{enumerate}
\item the forgetful functor $U_F:\Alg F \to \C$,
\item every concrete functor $T: \Alg F \to \Alg G$ (for every $G:\C \to \C$).
\end{enumerate}
\end{lm}
\begin{proo}
Let $J:\A \to \Alg F$ be a concrete functor and $\Ran_{U}U=(M,\epsilon)$. Due to the Remark \ref{transalg}, $J=(U,\iota)$ for some natural transformation $\iota:FU \to U$. Then $\epsilon:MU \to U$ yields the natural transformation $\iota \po F\epsilon:FMU \to U$. Hence there is a transformation $\upsilon:FM \to M$ such that the diagram
$$\xymatrix{
MU \ar[rr]^{\epsilon} &&U\\
FMU \ar[u]_{\upsilon U} \ar[rr]^{F\epsilon} && FU \ar[u]^{\iota}}$$
commutes.
We have gained a functor $V=(M,\upsilon):\C \to \Alg F$. The diagram above implies that the transformation $\epsilon$ can be extended to a transformation $\zeta :VU \to J$ such that $U_F \zeta=\epsilon$.

Let $G$ be another $\C$-endofunctor and let $U_G:\Alg G \to \C$ be the forgetful functor. Let $T=(U_F,\tau):\Alg F \to \Alg G$ be a concrete functor. We will show, that $(TV,T \zeta)$ is the right Kan extension of $TJ=(U,\tau J)$ along $U$.

Consider a functor $K=(U_G K, \kappa):\C \to \Alg G$ and a transformation $\lambda:KU \to TJ$. Then $U_G\lambda:U_G K U \to U$ is a natural transformation, hence there is $\rho:U_G K \to M$ such that $U_G \lambda = \epsilon \po \rho U$. Since $\lambda$ is the transformation $(U_G K U, \kappa U) \to (U_G TJ, \tau J)$, we have $U_G \lambda \po \kappa U = \tau J \po GU_G \lambda$.
The functor $T$ turns the diagram above into:
$$\xymatrix{
MU \ar[rr]^{\epsilon}&&U\\
GMU \ar[rr]^{G\epsilon}\ar[u]_{\tau VU} &&GU, \ar[u]^{\tau J} \\
}$$
hence $\tau J  \po G\epsilon = \epsilon \po \tau VU $.
We prove that $\rho$ underlies a transformation $K \to TV$.
$$\begin{array}{rcl}
\epsilon \po \rho U \po \kappa U &=& U_G \lambda \po \kappa U\\
&=& \tau J \po G U_G \lambda \\
&=& \tau J  \po G\epsilon \po G\rho U \\
&=& \epsilon \po \tau VU \po G\rho U.
\end{array}$$
Now from $(M, \epsilon)$ being the right Kan extension of $U$ along $U$, the uniqueness of factorization of a transformation $G U_G K U \to U$ over $\epsilon$ yields $\rho \po \kappa =\tau V \po G\rho$. Hence there is a transformation $\gamma:K \to TV$ such that $U_G \gamma = \rho$. Hence we have $U_G \lambda = \epsilon \po U_G \gamma U = U_G T\zeta \po U_G \gamma U$ which, due to faithfulness of $U_G$, implies
 $\lambda=T\zeta \po \gamma U$ and $(TV,T\zeta)$ becomes the right Kan extension of $TJ$ along $U$.

Since the procedure holds for every $G$ and $T$, by choice of $G=F$ and $T=\Id_{\Alg F}$ we get $(V,\zeta)=\Ran_U J$. For every other choice of $G,T$ we have $T\Ran_U J=T(V,\zeta)=(TV,T\zeta)=\Ran_U (TJ)$, hence $T$ preserves $\Ran_U J$.

Moreover $U_F\Ran_U J=U_F (V,\zeta)=(U_F V, U_F \zeta)=(M,\epsilon)=\Ran_U U$, hence even $U_F$ preserves $\Ran_U J$.
\end{proo}
\begin{note}
As pointed out by J. Velebil, since the whole proof is based only on the properties of functors and natural transformations, one can prove ana\-lo\-gous statement formally on the level of 2-categories.\end{note}
\begin{lm}\label{ranlim}
Let $(\A,U)$ be the limit of a diagram $D:\D \to \Con \C$, where $Dd$ is an f-algebraic category for each object $d$ of $\D$. If the codensity monad for $U$ exists, then $\Ran_U \Id_{\A}$ exists and is preserved by each component of the limiting cone $L_d:\A \to Dd$ $(d \in
\ob \D)$.
\end{lm}
\begin{proo}
If $\Ran_U U$ exists, then, for every $\D$-morphism $\phi:d \to d'$, the functor $D\phi:Dd \to Dd'$ is concrete between
f-algebraic categories, thus, due to Lemma \ref{ranconc}, $\Ran_U L_d$ and $\Ran_U L_{d'}$ exist and $\Ran_U
L_{d'}=D(\phi)\Ran_U L_d$. This is, due to the Remark \ref{compkancone}, equivalent to the existence of a componentwise right Kan extension of the cone $L$ along $U$. Then, by Theorem \ref{limkancone}, $\Ran_U \Id_{\A}$ exists and it is preserved by $L$.
\end{proo}
\begin{lm}
The forgetful functor $U$ of an l-algebraic category in $\Con \C$ with codensity monad creates the right Kan extension
of identity along $U$.
\end{lm}
\begin{proo}
If $(\A,U)$ is a limit of an empty diagram, then it is the terminal object of $\Con \C$, hence
$(\A,U)\cong (\C,\Id_C)$ and the situation is trivial.

Suppose $(\A,U)$ is a limit of a nonempty diagram and $\Ran_U U$ exists. The limiting cone is formed by f-algebraic categories $(\B_d,U_d)$ and concrete functors $L_d:\A \to \B_d$. Then according to the previous lemma, $\Ran_U Id$ exists and each functor $L_d$ preserves it. Moreover, due to Lemma \ref{ranconc}
each $U_d$ and the limiting cone $L_d$ preserves $\Ran_U L_d$,
hence their composition, which is equal to $U$, preserves $\Ran_U \Id$. Indeed, $U \Ran_U \Id =U_d L_d\Ran_U \Id \stackrel{\ref{ranlim}}{=}U_d
\Ran_U L_d \stackrel{\ref{ranconc}}{=} \Ran_U U_d L_d=\Ran_U U$.
\end{proo}

As a direct consequence of this lemma and the property of codensity monads we get the result:
\begin{theo}\label{codlcat}
Let $\A$ be an l-algebraic category. Then
\begin{center}
$\A$ has a codensity monad $\iff$ $\A$ has free objects.
\end{center}
\end{theo}

Since every monadic category is l-algebraic (see Lemma \ref{monad}), we get an alternative characterization of monadic categories:
\begin{theo}\label{monlcat}
Let $\A$ be a concrete category. Then
\begin{center}
$\A$ is monadic $\iff$ $\A$ is an l-algebraic category with a codensity monad.
\end{center}
\end{theo}
The statement cannot be extended to all Beck categories
unless the codensity monad is pointwise, as shown in the following example.
\begin{examp}\label{proti}
Consider the category $\C={\bf 2} + {\bf 2}$ consisting of objects $0,1,0',1'$ and morphisms $\iota:0 \to 1$, $\iota':0' \to 1'$ and identities. Let  $\A={\bf 1} + {\bf 1}$  and $U:\A \to \C$ be the inclusion of $\{0,0'\}$. Then the following holds:
\begin{enumerate}
\item \label{proti1}$(\A,U)$ is a Beck category.
\item \label{proti2}$(\A,U)$ has a codensity monad (the trivial monad).
\item \label{proti3}$U$ does not have an adjoint (1 does not have an universal arrow).
\end{enumerate}
\end{examp}

As a consequence, we see that there exists a codensity monad which is not pointwise and a Beck category that is not l-algebraic.
\section{Conclusion}
We have proved the propositions which, together with Beck's theorem, may be collected to the following theorem.
\begin{theo}
Let $\C$ be a category and $(\A,U)$ be concrete category over $\C$. The following statements are equivalent:
\begin{enumerate}
\item $\A$ is monadic.
\item $\A$ is Beck and $U$ has a left adjoint.
\item $\A$
is Beck and $U$ has a pointwise codensity monad.
\item $\A$ is l-algebraic and $U$ has a codensity monad.
\item $\A$ is an l-algebraic category with an $\Alg$-universal arrow.
\end{enumerate}
\end{theo}
\begin{rem}
If $\C$ has copowers, then we have even stronger result:
\begin{center}
$\A$ is a monadic category $\iff$ $\A$ is a Beck category with a codensity monad $\iff$ $\A$ is a Beck category with an $\Alg$-universal arrow.
\end{center}
\end{rem}
\paragraph{Acknowledgement} The author acknowledges partial support from Mi\-ni\-stry of Education of the Czech Republic, research plan no. MSM0021630518.

redpajama_set_name: RedPajamaArXiv


text:
Analysis: Mysterious Killing Rocks Montenegro
June 01, 2004 18:36 GMT
By Patrick Moore
Montenegrin authorities and German forensics experts are continuing their investigation of a killing that has mesmerized the small mountainous republic since late last week. Dusko Jovanovic, who was the chief and responsible editor of the opposition Podgorica daily "Dan," was killed in a drive-by shooting outside his offices late on 27 May. It is not known who killed Jovanovic or why, but speculation is rife in a country where talking politics is a national passion.
Shortly after the killing, investigating Judge Radomir Ivanovic said that he has several people in mind as suspects but did not elaborate. Montenegrin police found a car containing an automatic weapon in Podgorica on 29 May, both of which are believed to have played a role in the killing. German forensics experts subsequently arrived to help with the investigation. At least two individuals were taken into custody, both of whom appear to be linked to the car and its history and may not necessarily be suspected of involvement in the crime itself.
Prime Minister Milo Djukanovic, parliamentary speaker Ranko Krivokapic, journalists' professional associations, and opposition leaders were quick to condemn the killing, calling for the killers to be brought to justice. Interior Minister Dragan Djurovic offered a $1.2 million reward for information leading to solving the case, adding that he will resign if it remains unsolved. The government seemed to be at pains to show that it means business lest its reputation at home and abroad be damaged.
Montenegrin opposition parties held a candlelight vigil at the site of the shooting on 28 May. The previous evening, the opposition parties agreed they will continue to work to bring down Djukanovic's government, which they accused of corruption and involvement in criminal activities.
Jovanovic's funeral took place on 30 May, and the next day over 100 journalists attended a memorial meeting in his honor.
Speculation among the public at large and in much of the media turned to possible political motives behind the killing, with members of Jovanovic's own family hinting that unnamed people close to Djukanovic might have been involved. Lidija Bozovic, who handles "Dan's" legal affairs, said that Jovanovic had asked for police protection on several occasions but did not receive it. The police are known to be firmly under Djukanovic's control.
"Dan" generally reflects the views of the opposition, especially the Socialist People's Party (SNP), which was allied to the regime of former Yugoslav President Slobodan Milosevic. In the early 1990s, when Montenegro was a staunch ally of the Serbian leader, lawyer Jovanovic headed the Financial Police and then the Department of Public Revenues.
By 1997, Djukanovic decided that his and Montenegro's futures were best assured by breaking with Milosevic and appealing for Western support. When Djukanovic then solidified his grip on the governing Democratic Party of Socialists (DPS), Jovanovic and his allies, led by Momir Bulatovic, left it and founded the SNP. That party in turn split in 2001, following which Jovanovic left active politics.
In recent years, Jovanovic, "Dan," and the YU Media Mont company have been the object of at least 30 lawsuits stemming from charges published in the daily that Djukanovic has been involved in cigarette smuggling and human trafficking.
A Serbian court issued an arrest warrant for Jovanovic on charges that he embezzled $400,000 in 2000 from the Zastava plant in Kragujevac. The Hague-based war crimes tribunal indicted him for contempt of court for publishing in 2002 the name of a secret witness who testified against Milosevic, dropping the charge after Jovanovic apologized.
In short, Jovanovic was not quite the typical poster boy readily embraced by NGOs and Western governments in supporting crusading journalists in countries with questionable democratic credentials. His killing nonetheless seems to fit a pattern well-known to observers of Serbian politics, where many killings before and after the fall of Milosevic -- including those of some journalists -- remain unsolved (see "RFE/RL Balkan Report," 28 March, 9 May, and 12 December 2003).
But in Montenegro as in Serbia, caution is certainly in order in considering who might be behind a killing. Throughout much of former Yugoslavia, the worlds of politics, business, the security forces, and organized crime mix and move together in ways hidden from public view. What might seem at first glance to be a crime with an ethnic or political motive behind it, for example, could eventually prove to be rooted in murky business dealings or long-standing personal feuds. What does seem sure in this case, however, is that no one is likely to have undertaken lightly the killing of such a prominent individual as Jovanovic.
Whatever the motive for the crime, his fellow journalists tend to see his killing as a direct attack on the freedom of the press. Mili Prelevic, who is an editor of "Dan," said that the daily will continue to publish and to write about topics that interested Jovanovic. He told RFE/RL that the killing was a "terrorist crime," adding that the government must surely know who did it because Montenegro is a small country in which everyone knows everyone else's business.
Elsewhere, the Association of Journalists of Montenegro said in a declaration that Jovanovic's killing was an attack on the media as a whole. Association President Savo Gregovic stressed that the killing is a death blow to freedom of expression in Montenegro, which has long been under threat. He told RFE/RL that this "serious crime" shows that Montenegro is nothing like the solid democracy that the government claims it is.
European Commission spokeswoman Emma Udwin told MINA news agency by telephone that the report of Jovanovic's killing was "shocking news."

redpajama_set_name: RedPajamaCommonCrawl


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And as for the recent occurrences, turn to the relaters of our Hadiths for they are my proof upon you, and I am Allah's proof upon them. (Bihar al-Anwar Ch.53, P.181)
Let everyone of you do what ingratiates him with us and avoid what arises our aversion and displeasure with him. (Al-Ihtijaj, by al-Tabrasy Ch.2, P.324)
O Allah, fulfil your promise to me, complete my rule for me, increase my force and fill earth by me with justice and fairness. (Bihar al-Anwar Ch.51, P.31)
I bear witness that there is no god but He-and the angels, and men possessed of knowledge- upholding justice; there is no god but He the All-mighty, the All-wise; the true religion with Allah is Islam. (Bihar al-Anwar Ch.51, P.16)
I am Allah's Remainder (representative) in His earth, and the avenger on his enemies. (Tafseer Noor al-Thaqalayn Ch.2, P.392)
Our hearts are receptacles for Allah's will, so that if He wills we comply. (Bihar al-Anwar Ch.52, P.51)
Were it not for our desire to see you righteous and the mercy and pity we feel for you, we would have been too occupied to address you. (Bihar al-Anwar Ch.53, P.179)
I am al-Mahdi (the guided one), I am the imam of the time and I am the one who fills it (earth) with justice just as it was filled with injustice and tyranny. (Bihar al-Anwar Ch.52, P.2)
The oppressors alleged that Allah's proof is invalid, and if we were permitted to speak out, the uncertainty would disappear. (Bihar al-Anwar Ch.51, P.4)
We have comprehensive knowledge of your news, and not a thing of it escapes us. (Bihar al-Anwar Ch.53, P.175)
The faith is Muhammad's (his assignment), may Allah's prayers and peace be upon him and his household; and guidance is `Ali's, the Commander of The Believers, may peace be upon him, because it is meant for him and will remain in his descendants until the Day of Resurrection. (Bihar al-Anwar Ch.53, P.160)
And whoso oppresses us will be one of those who wrong us, and Allah's curse shall rest upon him because of the Almighty's saying, "Surely, Allah's curse shall rest upon the wrongdoers". (Bihar al-Anwar Ch.53, P.182)
If Allah permits us to speak, the truth would emerge and falsehood would vanish and be pulled away from you. (Bihar al-Anwar Ch.25, P.183)
And in the Prophet's daughter, may Allah's prayers and peace be upon him and his household, there is a good example. (Bihar al-Anwar Ch.53, P.180)
So fear God and submit to us, refer the matter to us, because we are the ones who execute Allah's commands as we were the ones who received them; do not try to uncover what was concealed from you and make your intention to love us according to the clear way. (Bihar al-Anwar Ch.53, P.179)
No manifestation but after Allah's permission, and that will be after the passing of a long term, the hardening of the hearts and the filling of earth with tyranny. (alehtejaj Ch.2, P.478)
There will come to my devotees those who will claim seeing (me). Verily, whosoever claims the seeing before the rising of al-Sofiany and the Cry, is a liar and a forger; and there is no power except with Almighty Allah. (alehtejaj Ch.2, P.478)
6. And through me shall Allah, the Mighty and Glorious, drive away the calamities from my progeny and my Shia's". (Bihar, V,52, P.30)
7. "Surely, I am indeed the (cause of) security for the inhabitant of the earth". (Bihar, V 53 p181).
8. "When Allah permits us to speak, truth will prevail and falsehood will vanish". (Bihar, V.53, p 196).
10. "Invoke more for the hastening of the re-appearance, for surely this is your safety". (Bihar).
11. "There were none of my fore fathers except that the allegiance of the oppressive rulers of their times was in their necks". (i.e. the previous Imams were forced to pay allegiance).
12. "As for deriving benefit from me in my occultation is like deriving benefit from the sun when it hides behind the clouds". (Bihar, V.53, p 181).
13. "And surely on my re-appearance, whenever I reappear, there will be no allegiance in my neck of any of the oppressive tyrants". (Bihar. V,53, p 181)
14. "If any incident occurs (now) then refer for it to the narrators of our traditions. For surely, they are my proof on you and I am the proof of Allah upon them". (Bihar, V. 53, p 181).
15. "For surely our knowledge encompasses information about you and none of your news is concealed from us". (Bihar, V. 53, p 175)
16. "Surely, we do not neglect your conditions nor are we forgetful of your remembrance". (Bihar, V. 53, p 175).
17. "Then each one of you should do those deeds which bring you closer to our love". (Bihar, V. 53, p 176).
18. "And you must refrain from (all such acts) which make you nearer to our displeasure and our anger". (Bihar 53/176).
20. "As for your wealth, we shall not accept it except that it should be purified (halaal). Then whoever wants, he can associate (with us) and whoever wants, he can sever". (Bihar, V 53 p 180).
21. "Whoever eats from our wealth (i.e. Khums) even an iota then he is taking fire in his abdomen and soon shall he be castled in it". (Bihar V.53, p 183).
22. "Allah's, the Mighty and the Glorious, Destinies are not overpowered, and His intentions are not rejected, and His Grace is not left behind". (Bihar 53/191).
23. "Seeking knowledge through any other means than us Ahle'Bait, tantamount to denial (in our mastership)". (Kitab Deen-o-Fitrat: Vol – 1)".
25. "(Allah) sent Mohammad (s.a.w.s) as a mercy unto the worlds and completed his bounties. Through him". (Bihar ,53/194).
26. "And He sealed through him (Mohammad S.A) His prophets and sent him to the whole of mankind". (Bihar 53/194).
29. "Certainly there is no (physical) relationship between Allah, Mighty and Glorious be He and anybody else". (Bihar 53/180)
35. "If you seek guidance you will be guided and if you search, you will find (the path)". (Kamaluddin Vol 2. P 502).
38. "Surely the truth is with us and in us and non can say like this except us. And if any one says then he is a liar a deceiver. None claims thus other than us except a strayed and lost one.
40. "If our Shias (May Allah give them opportunity of obedience) would be firm on their promises wholeheartedly, our meeting would not be delayed".
IMAM (A.S)'S ADDRESS TO HIS SHIAS :
"Then everyone of you shall act in a manner which makes him nearer to our love and refrain from those acts which makes him proximate to our dislike and our anger. For surely, our affair (re-appearance) will be sudden and unexpected when neither repentance shall benefit him nor shall remorse from sins save him from our chastisement".
"Nothing shall keep us away from the (Shias) except their news to us of those things which we dislike and do not expect from them. And Allah is the Helper.
The Qur'an says: "We sent forth Noah to his people, and he dwelt amongst them for one thousand years, less fifty." (29:14)
The Prophet (SAW) has been quoted as saying: "Isa (PBUH) the Son of Mary is not dead. Rather, before the Day of Resurrection, he will come back to you."
The late Allama Tabarsi says that the Prophet (SAW) has been quoted as saying: "How will it be when Isa, Son of Mary descends among you, when your Imam Mahdi (AS) has risen from among you." (Al-Bukhari, Isma'il ibn Ibrahim, Sahih Al-Bukhari, vol. 4, p. 205. Abul-Hussain, Muslim ibn Al-Hajjaj, Sahih Al-Muslim, vol. 1, p. 94)
The Need for Intercession in Seeking Divine Grace:
A very important issue to refer to here is the need for intercession in seeking Divine Grace. We read in the Qur'an:
"O you who believe! Have fear of Allah and seek the means by which you get His favor." (5:35)
Sheikh Saduq quotes Sulaiman ibn Ja'afar as saying: "I asked Imam Reza (AS). Will the earth ever be devoid of a sign of God?"
The Imam replied: "Even if that were to happen for as long as the blinking of an eye, the earth would cave in with all its inhabitants." (Sheikh Saduq, "Uyun-e-Akbar al-Reza", pp. 150-151)
Elsewhere he quotes Imam Baqir (AS), saying: "If the earth would be devoid of an Imam from our Household for even a single day, it would swallow in all its inhabitants. And Allah would afflict the dwellers of the earth with a severe punishment. The Lord Almighty has appointed us as this sign and for the safety of the dwellers of the earth. As long as we live among them, those who would otherwise be swallowed into the earth are in safety." (Sheikh Saduq, Kamal ad-Din wa Tamam an-Ne'ma, pp. 150-151)
Thus, in the same way that these Imams are intercessors for the True Religion, they are also the intercessors for Grace and Earthly and Heavenly abundance for mankind.
Imam Ja'far al Sadiq (A.S.) is also reported to have said:
"I see the Mahdi and his companions as if they are threatened by danger from all sides: their supplies have exhausted; their clothes have worn out; their foreheads bear the mark of prostration; during the day they are as courageous as a lion and during the night they are busy in the adoration of Allah; and their hearts are like solid pieces of iron".
Anyhow, all these sacrifices and hardships will have a happy end.
Imam Ja'far al Sadiq (A.S.) has said:
"It is true that the righteous always lead a hard life. But the end of their hardship is not far off".
Nevertheless the success of the Mahdi will be largely due to invisible Divine help. Many traditions bear witness to that.
As a result of these sacrifices and the Divine help real Islamic rule will be established. These are some of the reports which throw light on the doctrinal and social system which will follow.
Explaining the Qur'anic verse, It is Allah who sent His Messenger with guidance and true religion that He might make it victorious over all religions, howsoever the unbelievers might be averse, Imam al Sadiq (A.S.) said: "This verse will come true only during the time of the Mahdi, when the unbelievers will no longer exist".
At present Islam has been surrounded by some people with so many myths and doubts that it appears to be some different religion. This position will continue till the Mahdi rises.
"As soon as the Mahdi rises, he will introduce a new system as the Prophet had done in the beginning of Islam".
"The Mahdi will do what the holy Prophet had done. He will smash the existing system in the same way as the holy Prophet had shattered the pre-Islamic pagan system, and replaced it by Islam".
The new system introduced by the Mahdi will be so queer to some of those who claim to be the champions of religion and to be having full knowledge of it that they will pick up a row against him but they will not be able to resist the divine world movement and will be annihilated.
At the end of a detailed talk, Imam Baqir (A.S.) said:
"On an occasion when the Mahdi will be busy narrating Divine commands and speaking about the practice of the holy Prophet and the Imams, an attack on him will be arranged from within the places of worship. The Imam will order his followers to arrest the insurgents and put them to death. This will be the last hostile action against the Mahdi".
When the evil-doers will have been crushed and the correct Islamic attitude popularised, the atmosphere will become conducive to intellectual growth and expansion of knowledge.
Imam Ali (A.S.) is reported to have said:
"I see a large number of tents pitched, and people under them being taught the Qur'an in the same order in which it was revealed".
In the course of a talk about that period Imam Muhammad al Baqir (A.S.) said:
"Knowledge will become so common that even women will give decisions on the basis of the Qur'an and the Sunnah of the holy Prophet".
Knowledge in various fields will expand. The total of the discoveries of the past will bear no comparison to the discoveries made during that period.
According to a report, Imam Ja'far al Sadiq (A.S.) explained the position allegorically. He said: "If the total of possible human knowledge is supposed to be seventy two letters, two letters will have been known up to that time and the remaining seventy will be discovered gradually during that period".
In respect of the intellectual and moral development of the people, Imam Muhammad al Baqir (A.S.) has said:
"When our Qaim will rise and the people will come under his protection, their intellectual faculties will bloom and their human qualities will be perfected and will bear fruit".
During that period the under-privileged masses will be the masters of the power and wealth of the world. Many reports say that the following verse relates to that period: "We willed to show favor to those who were persecuted in the land and make them rulers and heirs o f the land, and give them power and wealth of the earth ". (Surah al-Qasas, 28:5).
A Signed Proclamation from Imam Mahdi (A.S.)
Though at present we are living away from the dominions of the oppressors and till the unjust rule the world, the Almighty has considered it better for us and our Shias that I stay away from them. But despite this separation, I am cognizant of all your affairs. Nothing pertaining to you is hidden from us. Whenever you experience insults, I come to know of it. This is from the time some of you began to do those acts which were shunned by your ancestors. These people have thrown behind their covenant with Allah as if it had never been made.
We are never negligent in your protection nor are we forgetful of your remembrance. (If our protection and guidance had not been there) misfortunes would have befallen you and the enemies would have destroyed you. Be fearful of Allah and help us (our cause) which will save you from the corruption that has surrounded you.
Soon, clear signs from the heavens will be manifested for you and signs will appear on the earth as well. Disastrous and sorrowful incidents will occur in the east. Thereafter, Iraq will be ruled by people who are completely away from Islam. Due to their vile deeds, the people of Iraq will experience an acute shortage of sustenance. Then after a long time, when the tyrannical rulers perish, the people of Iraq will be rescued from their difficulties. After the annihilation of the tyrants, the pious and the good people shall rejoice.
People from every corner of the world who go to perform Hajj (the annual pilgrimage) will achieve all their desires and get whatever they wish. As per their wishes, their Hajj will be made easy through our worth and position. It will be manifested in our systematic manner.
Thus each of you should perform such deeds that bring you closer to our love and avoid those acts which result in our anger and dissatisfaction. For, our reappearance will be sudden and unexpected when repentance will be of no use nor shall remorse for sinful deeds (at that time) save you from our punishment.
May Allah show you the path of true guidance and by His Mercy bestow you the means of Divine Grace (Tawfeeq).
[Tawqee of Hazrat Vali-e-Asr (a.t.f.s.) addressed to the respected Shaykh al-Mufeed (ra-)]
The Signs of the Reappearance of Imam Mahdi (A.S.)
The Signs of the Reappearance (Qiyam) of the (Imam) who undertakes the Office (Al-Qa'im), Peace be on him, the Period of Time of his Appearance, an Explanation of his Life and an Extract of what is revealed about his State.
Traditions have been reported mentioning the signs for the time of the appearance of the Imam who will arise (qa'im), peace be on him, and the events which will take place before his appearance, together with the indications and features of it. Among them are:
"The Sufaini will come out in revolt; the Hassani will be killed; the 'Abbasids will dispute over worldly kingdom; there will be an eclipse of the sun in the middle of the month of Ramadan; there will be an eclipse of the moon at the end of that month in contrast to ordinary happenings; the land will be swallowed up at al-Bayda'; it will be swallowed in the east; it will be swallowed up in the west; the sun will stay still from the time of its decline to the middle of the time for the afternoon prayer; it will rise from the west; a pure soul (Nafs zakiyya) will be killed in the outskirts of Kufa with seventy righteous men; a Hishimite will be slaughtered between the corner of the Ka'bah, and the station of Prophet Abraham; the wall of the mosque of Kufa will be destroyed; black standards will advance from Khurassan; al-Yamani will come out in revolt; al-Maghribi will appear in Egypt and take possession of it from Syria; the Turk will occupy the region of al-Jazira; the Byzantines will occupy Ramala; the star will appear in the east giving light just like the moon gives light; then (the new moon) will bend until its two tips almost meet; a colour will appear in the sky and spread to its horizons; a fire will appear for a long time in the east remaining in the air for three or seven days; the Arabs will throw off the reins and take possession of their land, throwing out the foreign authority; the people of Egypt will kill their ruler and destroy Syria; and three standards will dispute over it (Syria); the standards of Qays and the Arabs will come among the people of Egypt; the standards of Kinda (will go) to Khurasan; horses will come from the west until they are stabled in al-Hira; the black standards will advance towards them from the east; the Euphrates will flood so that the water comes into the alleys of Kufa; sixty liars will come forward, all of them claiming prophethood, and twelve will come forward from the family of Abu Talib, all of them claiming the Imamate; a man of important rank of the supporters of the `Abbasids will be burnt between Jalula` and Khaniqin; the bridge next to Karkhin the city of Baghdad will be established; a black wind will raise it at the beginning of the day and then an earthquake will occur so that much of it will be swallowed up; fear will cover the people of Iraq and Baghdad; swift death (will occur) there and there will be a loss of property, lives and harvests; locusts will appear at their usual times and at times not usual so that they attack agricultural land and crops and there will be little harvest for what the people planted; two kinds of foreigners will dispute and much blood will be shed in their quarrel; slaves will rebel against obedience to their masters and kill their masters (mawali); a group of heretics (ahl al-bida) will be transformed until they become monkeys and pigs; slaves will conquer the land of their masters; a cry (will come) from the sky (in such a way) that all the people will hear it in their own languages; a face and a chest will appear in the sky before the people in the centre of the sun; the dead will arise from their graves' so that they will return to the world and they will recognize one another and visit one another; that will come to an end with twenty four continuous rainstorms and the land will be revived by them after being dead and it will recognize its blessings; after that every disease will be taken away from those of the Shi`a of the Mahdi, peace be on him, who believe in the truth; at that time they will know of his appearance in Mecca and they will go to him to support him."
(These signs) are as the reports have mentioned. Among the total of these events are some which are bound (to happen) and other which are conditional. God knows best what will take place. We have only mentioned them on the basis of what is recounted in basic sources of tradition because of their inclusion in traditions which have been handed down. From God we seek help and Him do we ask for success.
Abu al-Hasan Ali b. Bilil al-Muhallabi informed me: Muhammad b. Ja'far al-Mu'addib told me on the authority of Ahmad b. Idris, on the authority of `All b. Muhammad b. Qutayba, on the authority of al-Fadl b. Shidhan, on the authority of Ismail b. al-Sabbih, who said: I heard an old man among our colleagues mention on the authority of Sayf b. Umayra, who said:
I [Sayf b. Umayra] was with Abu Ja'far al-Mansur and he said to me of his own accord: "There will certainly be a voice calling from the sky the name of a man from the descendants of Abu Talib."
"May I be your ransom, Commander of the faithful," I said, "do you relate that?"
"Indeed, by Him in Whose hands is my life," he replied, "because my own ears have heard it."
"Commander of the faithful," I said, "this tradition which you have heard is before my time."
"Sayf, it is the truth," he told me. "When it happens, we will be the first to answer it. Indeed the call will be for a man from the descendants of our uncle."
"A man from the descendants of Fatima, peace be on her?" I asked.
"Yes," he replied. "Sayf, if it was not for the fact that I have heard from Abu Ja`far Muhammad b. 'Ali (al-Baqir), who told me about it, even though all the people of the earth have told me about it, I would not accept it from them. However it was Muhammad b. `Ali (al-Baqir), peace be on them, (who told me)."
Yahya b. Abi Talib reported on the authority of Ali b. Asim, on the authority of Ata' b. al-Sa'ib, on the authority of his father on the authority of Abd Allah b. Umar, who said:
The Apostle of God, may God bless him and his family, said: "The hour (of the end of the world) will not arise until the Mahdf from my descendants comes forth. The Mahdi will not come forth until sixty liars come forward, all of them declaring: "I am a prophet."
al-Fadl b. Shadhan reported on the authority of one who reported it on the authority of Abu Hamza al-Thumali, who said:
I (i.e. Abu Hamza al-Thumali) asked Abu Ja`far (Imam al-Baqir), peace be on him: "Is the revolt of the Sufyani one of the things which must happen?"
"Yes," he replied. "The call is one of the things which must happen as is the rising of the sun from the west one of the things which must happen. The dispute of the `Abbasids over the state is also one of them and the killing of the pure soul (al-nafs al-zakiyya). The appearance of the one who will arise (al-qa'im) from the family of Muhammad, may God bless him and his family, is another of the things which must happen."
"How will the call be?" I asked.
"There will be a call from the sky at the beginning of the day indeed the truth is with `Ali and his Shi'a," he said. "Then at the end of the day, Satan will call from the earth - indeed the truth is with 'Uthman and his supporters. At that the false one will feel doubt."
Al-Hasan b. Ali al-Washsha' (reported) on the authority of Ahmad b. A'idh, on the authority of Abu Khadija, on the authority of Abu Abd Allah (Imam Jafar al-Sadiq, peace be on him):
Imam Ja'far al-Sadiq said: "The one who will arise (al-qa'im) will not come forth until twelve of the Banu Hashim come forth before him, all of them summoning men to themselves."
Muhammad b. Abi al-Bilad (reported) on the authority of `All b. Muhammad al-Azdi, on the authority of his father, on the authority of his grandfather, who said:
The Commander of the faithful, Imam Ali, peace be on him, said: "Before the one who will arise (al-qa'im), there will be red death and white death; there will be locusts at their usual time and at their unusual time like the colours of blood. As for red death that is (from) the sword, while white death is (from) plague."
Al-Hasan b. Mahblib (reported) on the authority of Amr b. Abi Miqdam, on the authority of Jabir al-Ju`fi, on the authority of Abu Ja'far (Imam al-Baqir), peace be on him:
Imam Muhammad AI-Baqir said: "Stay close to the ground. Don't move an arm or a leg until you see the signs which I will mention to you - I don't think that you will live until that time. The `Abbasids will dispute; a voice will call from the sky; one of the villages of Syria called al-Jabiyya will be swallowed up; the Turks will occupy the region of al-Jazua; the Byzantines will attack al-Ramla; at that time there will be much conflict throughout the land until Syria is destroyed. The cause of its destruction will be the meeting of three standards there: the standard of the Red, the standard of the Spotted and the standard of the Sufyani."
Ali b. Abi Hamza (reported) on the authority of Abu al-Hasan Musa, peace be on him:
Concerning the words of Him, the Mighty and High: "We will show them our signs on the horizons and in themselves so that it will become clear to them that it is the truth (XLI 53). (Musa) said: "There will be a disturbance on the horizons and the enemies of truth will be changed in form."
Wahb b. (Abi) Hafs (reported) on the authority of Abu Bajr, who said:
I (Abu Basir) heard Abu Ja'far (Imam al-Baqir) speak concerning the words of Him, the Exalted: "If We wish, We will send down on ahem signs from the sky, and their necks will remain bent submissively to them (XXVI d)" He said: "God will do that to them."
"Who are they?" I asked.
"The Umayyads and their supporters," he answered.
"What is the sign?" I asked.
"Between the decline of the sun (at noon) and the time of the afternoon prayer, the sun will remain still," he said. "The chest and face of man will appear in the centre of the sun, who will be recognized by his standing and genealogy. That will occur in the time of the Sufyani. At that moment his destruction will occur and the destruction of his people."
Abd Allah b. Bukayr (reported) on the authority of Abd alMalik b. Isma'il, on the authority of his father, on the authority of Said b. Jubayr:
Sa'id b. Jubayr, said: "In the year in which the Mahdi will rise, twenty rain storms will rain on the earth. You will see their effects and benefits."
Al-Fadl b. Shadhan (reported) on the authority of Ahmad b. Muhammad b. Abi Nasr, on the authority of Tha'laba al-Azdi, who said:
Abu Ja'far (al-Baqir), peace be on him, said: "Two signs will come before the one who will arise (al-Qa'im), peace be on him: there will be an eclipse of the sun in the middle of the month of Ramadan and an eclipse of the moon at the end of it."
"Son of the Apostle of God," I said, "usually the eclipse of the sun occurs at the end of the month and the eclipse of the moon occurs in the middle of it?"
"I know what I have said," replied Abu Ja'far (Imam al-Baqir), peace be on him. "They are signs which have not occurred since Adam came down."
Tha'laba b. Maymun (reported) on the authority of Shu'ayb alHaddad, on the authority of Salih b. Maytham, who said:
I (i.e. Salih b. Maytham) heard Abu Ja`far (al-Baqir), peace be on him, say: "There is no longer than fifteen nights between the appearance of the one who will rise (al-qaim), peace be on him, and the killing of the pure soul (al-nafs al-zakiyya)."
Amr b Shamir (reported) on the authority of Jabir (al-Ju'fi), who said:
I (i.e. Jabir al-Ju'fi) said to Abu Ja'far (Imam al-Baqir), peace be on him: "When will this event occur?"
"Jabir, that will occur at a time when the killing between al-Hira and Kufa is considerable," he replied.
Muhammad b. Sinan (reported) on the authority of al-Husayn b. al-Mukhtar, on the authority of Abu Abd Allah (Imam Ja'far al-Sadiq),peace be on him:
(Imam Ja'far al-Sadiq) said: "When the wall of the mosque of Kufa, which adjoins the house of `Abd Allah b. Mas'ud is destroyed, then at that time the ruler of the people will disappear. At his disappearance, the one who will rise (al-qa'im), peace be on him, will come forth."
Sayf b. Umayra (reported) on the authority of Bakr b. Muhammad, on the authority of Abu Abd Allah (Imam Ja'far al-Sadiq), peace be on him:
(Imam Ja`far al-Sadiq) said: "There will be three appearances in one year, one month and one day - the Sufyani, the Khurasani and the Yamini. The standard of guidance will not be among them, except the standard of the Yamani, because he will summon (people) to the truth."
Al-Fadl b. Shadhan (reported) on the authority of Ahmad b. Muhammad b. Abi Nasr, on the authority of Abu al-Hasan al-Ridha, peace be on him:
Al-Ridha said: "What you stretch your necks for will not occur until you are able to discern and to be tested. Only a few of you will remain."
Then he recited: Alif Lam. Do the people consider that they can abandon saying "We believe whenever they are tempted? (XXIX, 1-2). He said: "Among the signs of the relief is an event which will occur between the two mosques (of Mecca and Medina). So-and-so from the descendants of so-and-so will kill fifteen leaders of the Arabs."
Al-Fadl b. Shadhan (reported) on the authority of Mu'ammar b. Khallad on the authority of Abu al-Hasan (al-Rida), peace be on him:
Al-Ridha said: "It is as if I see standards, dyed green, coming from Egypt until they come to the Syrian (standards). Then they will be guided to the descendant of the one who gave the testamentary bequests of authority (to the Imams)."
Hammed b. Isa reported on the authority of Ibrahim b. `Umar al-Yamani on the authority of Abu Basil, on the authority Imam Ja'far al-Sadiq, peace be on him:
Imam Jafar al-Sadiq said: "The kingdom of these men will not disappear until they slaughter people in Kufa on Friday. It is as if I was looking at heads falling between the Gate of al-1711 and (the place of) the soap-sellers."
Ali b. Asbat reported on the authority of Abu al-Hasan b. al-Jahm, who said:
A man asked Abu al-Hasan (Imam Musa Al-Kazim), peace be on him, about the relief. He asked: "Do you want most of it or shall I give you a summary?"
"Would you give me a summary?" he said.
"It will be when the standards of Qays are carried in Egypt and the standards of Kinda in Khurasan," he replied.
AI-Husayn b. Abi Ali reported on the authority of Abu Basir, on the authority of Imam Ja'far al-Sadiq, peace be on him:
Imam Ja`far al-Sadiq said: "Because of the sons of so-and-so there will be a battle at your mosque - meaning the mosque of Kufa. On one Friday four thousand will be killed between the Gate of al-Fil to (the place of) the soap-sellers. Beware of this street. Avoid it. Those who are in the best situation will take the street of the Ansar."
Ali b. Abi Hamza (reported) on the authority of Abu Basir, on the authority of Imam Ja'far al-Sadiq, peace be on him:
Imam Ja`far al-Sadiq said: "Before (the coming of) the one who will rise (al-Qa'im), peace be on him, there will be a year of abundant rain in which the fruits and the dates on the palms will be destroyed. But don't complain of that."
Ibrahim b. Muhammad (reported) on the authority of Ja'far b. Sa'd, on the authority of his father, on the authority of Imam Ja'far al-Sadiq, peace be on him:
Imam Ja'far al-Sadiq said: "In the year of the Conquest (by the Mahdi) the Euphrates will flood so that the water goes into the alleys of Kufa."
It is reported in the account (Hadith) of Muhammad b. Muslim, who said:
I (i.e. Muhammad b. Muslim) heard Imam Ja'far al-Sadiq, peace be on him, say: "Before (the coming) of the one who will rise (al-qa'im) there will be a trial from God."
"May I be your ransom, what is that?" I asked him.
He recited: "Let Us test you with fear, with hunger, and with lack of money, of lives and of harvests. Good news will come to those who are steadfast (11155)." Then he said: "The fear will be from the kings of the Banu so-and-so; the hunger will be as a result of exorbitant prices; the lack of money will be due to the failure of trade and the scarcity of surplus (goods) in it; the lack of lives will be because of swift death; the lack of harvest will be due to the great rains and the little benefit they bring to the crops." Then he continued: "The good news for those who are steadfast is that the one who will rise (al-qa'im) will soon come forth."
AI-Husayn b. Sai'd reported on the authority of Mundhir Al-Jawzi, on the authority of Imam Ja'far al-Sadiq, peace be on him:
Mundhir al-Jawzi said: I heard Imam Ja'far al-Sadiq say: "Before the coming of the one who will rise (al-qa'im), peace be on him, the people will be chided for their acts of disobedience by a fire which will appear in the sky and a redness which will cover the sky. It will swallow up Baghdad, it will swallow up Kufa. Their blood will be shed and houses destroyed. Death (fans) will occur amid their people and a fear will come over the people of Iraq from which they shall have no rest."
The Messianic Leader, Mahdi, in Other Religions
Engineer Madani: Is belief in the promised Mahdi confined to the followers of Islam, or does it exist in other religions too?
Mr. Hoshyar: In fact, this belief is not limited to the Muslims alone. In almost all religions and heavenly creeds one can find a similar belief in the future savior. The followers of these religions believe that there will come a time when the world will become corrupt and engulfed in a crisis. Evil and injustice will become the rule of the day. Disbelief will cover the entire world. At that time, the universal savior of the world will appear. With remarkable divine help he will restore the purity of faith and defeat materialism with the help of divine worship. Not only are the tidings to be found in revealed books like the Zand and Pazand, and Jamaspname of the Zoroastrians, the Torah and other Biblical books of the Jews, and the Gospel of the Christians, such information can also be seen, more or less, among the Brahmins and the Buddhists.
The followers of all religions and traditions maintain such a belief and are awaiting the appearance of such a commanding figure under the divine protection. Each tradition recognizes this figure with a different name and specific title. The Zoroastrians call him Saoshyant (meaning the 'saviour of the world'); the Jews know him as the messiah, whereas the Christians regard him as the Saviour Messiah. However, each group believes that this divinely ordained saviour will be among them. The Zoroastrians believe he is Persian and among the followers of Zoroaster. The Jews maintain that he will be among the Children of Israel, and the follower of Moses. The Christians think he will be one among them. Muslims believe that he will be among the Hashimites and among the direct descendants of the Prophet. In Islam he has been fully introduced, whereas in other religions this is not so.
It is remarkable that all the characteristics and signs mentioned for this universal saviour in other religions are applicable to the promised Mahdi, the son of Imam Hasan 'Askari. It is possible to regard him as Iranian in race because among his ancestors is the mother of the fourth Imam Zayn al-'Abidin who, as the daughter of Yazdgard, the Sassanian king, was a Persian princess. He can also be considered among the Children of Israel, since both the Hashimites and the Israelites are among the descendants of Abraham. The Hashimites are the descendants of Isma'il (Ishmael) and the Israelites are the descendants of Ishaq (Isaac). Hence, the Hashimites and the Israelites are one family. He is also connected to Christians because, according to some traditions, the mother of the present Imam was a Byzantine princess by the name of Narjis (Nargis), who is part of the miraculous story reported in some sources.
It is not appropriate to confine the deliverer of the world, the Mahdi, to one particular nation. He will actually come to fight against all discriminatory claims of racial, creedal and national distinction. Consequently, he should be regarded as the Mahdi of the whole of humanity. He is the saviour and deliverer of the people who worship God. His victory is the victory of all the prophets and all the righteous ones on earth. He will be restoring the religion of Abraham, Moses, Jesus and all of the heavenly revelations, namely, Islam; he will revive the pure religion of Moses and Jesus which had foretold the prophethood of Muhammad.
Let us be clear that we have no intention of proving the existence of the promised Mahdi by referring to the ancient books, nor are we in need of doing so. Our intention is to demonstrate that the belief in the appearance of the unique saviour of the world is a common religious belief, stemming from divine revelation, of which all prophets gave glad tidings. All nations are awaiting his emergence, but they have made errors in identifying him.
Imam Al-Mahdi, The Just Leader of Humanity
By:Ayatollah Ibrahim Amini


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Taking Offense at Every Word or Phrase?
William F. Shughart II • Monday August 11, 2014 4:37 PM PDT •
A recent news item suggests that if offense possibly can be taken, it will be taken.
We have just been treated to studied outrage at the nicknames of the NFL's Washington "Redskins", Florida State University's "Seminoles" and MLB's Cleveland "Indians." As my friend and colleague Randy Holcombe reminds us in a recent blog, the moniker of the "New York Yankees" may be more offensive to southerners than any of those names.
News reports now suggest that a small cadre of faculty members at the University of Mississippi want to ban the use of "Ole Miss" as the school's nickname owing to its "racist" origins. Never mind that a survey conducted by the university itself found that a majority of respondents reported that "Ole Miss" was nothing more than convenient shorthand for "The University of Mississippi" (and it fits better on football helmets and baseball and basketball jerseys).
What is the origin of "Ole Miss"? Slaves coined it, in reference to the wife of the planter to whom they were bound. If the planter and his wife had a daughter, she was called the "young miss." The term, hence, did originate in the slave culture of the cotton south, but its racist connection is indirect insofar as it grew from the linguistic usages of the slaves themselves. (Truth in advertising: Until 2011, I was on the faculty at the University of Mississippi for 23 years; I am a Rebel as well as an Aggie.)
Slavery and "Ole Miss" are anachronisms, but history happened and cannot be expunged by linguistic revisionism, unless we are willing to establish an Orwellian Ministry of Truth that erases our collective memory. Ole Miss already has banned the Beauregard ("Rebel") flag and "Colonel Reb" as its on-field mascot, substituting for them a black bear having no historical context other than a possibly apocryphal bear-shooting visit to the state by Teddy Roosevelt.
The University of Utah just reached an agreement with the "Utes" allowing the school to continue to use its nickname in return for a promise of college scholarships earmarked for members of that tribe of Native Americans. I suspect that a payoff in cash or in kind likewise is the underlying goal of individuals and groups opposed to "Ole Miss."
William F. Shughart II is a Senior Fellow at the Independent Institute, the J. Fish Smith Professor in Public Choice at Utah State University, past President of the Southern Economic Association, and editor of the Independent book, Taxing Choice.
Posts by William F. Shughart II | Full Biography and Publications
Affirmative Action Censorship college Native Americans political correctness Public Opinion Slavery


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Serious Coronavirus Cases Drop to their Lowest in Two Months
According to the figures published on Thursday by the Health Ministry, the number of coronavirus patients in serious condition continued to fall, as it reached 403, which is the lowest it has been in the last two months. In another sign that the fourth wave of COVID-19 in Israel is receding, the positive test rate for coronavirus cases had also fallen to 1.73% a day earlier. This means that Wednesday was the fifth day in a row that saw results below 2%, as compared to a month ago when it had been 7%. A total of 100,760 tests for the coronavirus were conducted and 1,732 of them came back positive.
The update from the ministry also indicated that the previous 24 hours had not seen anyone die from the virus, which was the first time to have happened since July. The total number of deaths due to COVID-19 in the country remained at 7,959. The number of serious patients is considered an important indicator of the spread of the virus and officials have been looking forward to see the numbers go down. However, Nachman Ash, the Director-General of the Health Ministry, said that despite the positive data, they will not remove some of the restrictions because they want to prevent the spread of the infection.
Ash said that there was no doubt that the number of infections in the fourth wave of the coronavirus were declining. He also highlighted that health officials had been concerned about the beginning of the school year in September because they had thought it would lead to a spike in cases. But, it hadn't turned out to be a setback as expected. Ash said that they had come far enough from the beginning of classes and the number of confirmed cases as well as serious patients has gone down. He added that they were on a downward track and this was a good thing.
According to him, the Health Ministry is trying to come up with ways for lifting some of the rules that were imposed for curbing infections, but they also don't want another outbreak to happen. After all, restrictions had been lifted back in June rather swiftly and this had led to the current wave of the virus, along with the highly infectious Delta variant of the virus. He added that face masks would remain compulsory throughout the winter in public enclosed spaces. He said that it was a simple and important way of preventing infections, which includes the flu.
Likewise, other rules that restrict access of people to public spaces will continue to be followed for the time being. Citizens are required to have the Green Pass in order to gain access, as it confirms recovery from COVID-19, vaccination against the virus as well as a recent negative test of the virus. According to Ash, they were still assessing a plan for replacing the quarantine of school kids with daily tests after being exposed to the virus and they would see the results of the pilot program next week.
Previous Millions of COVID-19 Test Kits Arrive In Israel for Schoolchildren
Next PM Pushing for Easing of COVID-19 Curbs


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Are Students Loans Preventing College Grads From Buying Homes?
It's often said that gaining a four-year education is the way to properly enter adulthood. College graduates are experiencing difficulties more than non college-grads because they are in a deep hole of student loan debt. It is problematic for thousands of folks trying to make it these days, especially with the decline in the economy.
The real problem with college loans being so difficult to repay quickly. Buying a home is something many young people want to do, and feel that they have earned after studying for four years and doing the work it takes to graduate—sadly, most will not have that opportunity unless federal law changes loan interest rates.
The heavy loans are more common than one might think: seven out of 10 college graduates leave school with a huge bill and growing interest rates. It's tough to move on in life, financially and otherwise, when loan debt is hovering like a dark cloud over every step of your journey. Many students and non-students alike wonder whether the burden of such an expensive loan is worth the education they'll receive. After all, garnering a Bachelor's degree does not guarantee employment whatsoever.
For some, it is worth the long task of repaying student loans. For others, this is simply not the case. Depending on the type of career desired, a college education is not necessarily always needed. Many college-aged people see their friends graduating and are shocked how much money they have to pay back.
Some preoccupy themselves with worry concerning the wealth gap in the United States. It seems that student debt may be driving a wedge between those who are wealthy enough to pay their loans back and others who might be paying back their loans until the day they die.
A person who isn't buried in student loan debt is likely to invest their money in a home.