Definition:Morphism of Cones

Definition
Let $\mathbf C$ be a metacategory.

Let $D: \mathbf J \to \mathbf C$ be a $\mathbf J$-diagram in $\mathbf C$.

Let $\left({C, c_j}\right)$ and $\left({C', c'_j}\right)$ be cones to $D$.

Let $f: C \to C'$ be a morphism of $\mathbf C$.

Then $f$ is a morphism of cones iff, for all objects $j$ of $\mathbf J$:


 * $\begin{xy}\xymatrix@+0.5em@L+2px{

C \ar[r]^*+{f} \ar[dr]_*+{c_j} & C' \ar[d]^*+{c'_j} \\ & D_j }\end{xy}$

is a commutative diagram.