Definition:Category of Cones

Definition
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:

By Category of Cones is Category, it is in fact a category.