\begin{definition}[Definition:Category of Cones]
Let $\mathbf C$ be a metacategory.
Let $D: \mathbf J \to \mathbf C$ be a $\mathbf J$-diagram in $\mathbf C$.
The '''category of cones to $D$''', denoted $\mathbf{Cone} \left({D}\right)$, is defined as follows:
{{DefineCategory
| ob = The cones to $D$
| mor = The morphisms of cones
| comp = Composition in $\mathbf C$
|id = $\operatorname{id}_{\left({C, c_j}\right)} := \operatorname{id}_C$, for a cone $\left({C, c_j}\right)$
}}
\end{definition}