\begin{definition}[Definition:Functor Creating Colimits]
Let $\mathbf C, \mathbf D$ and $\mathbf J$ be metacategories.
Let $F: \mathbf C \to \mathbf D$ be a functor.
Then $F$ is said to '''create colimits of type $\mathbf J$''' {{iff}}:
:For all $\mathbf J$-diagrams $C: \mathbf J \to \mathbf C$ in $\mathbf C$, given a colimit $\paren {{\varinjlim \,}_j \, FC_j, q_j}$ for $FC: \mathbf J \to \mathbf D$ in $\mathbf D$, the colimit:
::$\paren {{\varinjlim \,}_j \, C_j, p_j}$
:exists, and furthermore:
::$\map F {{\varinjlim \,}_j \, C_j} = {\varinjlim \,}_j \, FC_j$
::$F p_j = q_j$
:for all objects $j$ of $\mathbf J$.
\end{definition}