\begin{definition}[Definition:Limit (Category Theory)]
Let $\mathbf C$ be a metacategory.
Let $D: \mathbf J \to \mathbf C$ be a $\mathbf J$-diagram in $\mathbf C$.
Let $\mathbf{Cone} \left({D}\right)$ be the category of cones to $D$.
A '''limit for $D$''' is a terminal object in $\mathbf{Cone} \left({D}\right)$.
It is denoted by $\varprojlim_j D_j$; the associated morphisms $p_i: \varprojlim_j D_j \to D_i$ are usually left implicit.
\end{definition}