\begin{definition}[Definition:Morphism of Cocones]
Let $\mathbf C$ be a metacategory.
Let $D: \mathbf J \to \mathbf C$ be a $\mathbf J$-diagram in $\mathbf C$.
Let $\struct {C, c_j}$ and $\struct {C', c'_j}$ be cocones from $D$.
Let $f: C \to C'$ be a morphism of $\mathbf C$.
Then $f$ is a '''morphism of cones''' {{iff}}, for all objects $j$ of $\mathbf J$:
::$\begin{xy}\xymatrix@+0.5em@L+3px{
 D_j
  \ar[d]_*+{c_j}
  \ar[dr]^*+{c'_j}
\\
 C
  \ar[r]_*+{f}
&
 C'
}\end{xy}$
is a commutative diagram.
\end{definition}