Definition:Functor Creating Colimits

Definition
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 $\left({{\varinjlim \,}_j \, FC_j, q_j}\right)$ for $FC: \mathbf J \to \mathbf D$ in $\mathbf D$, the colimit:


 * $\left({{\varinjlim \,}_j \, C_j, p_j}\right)$


 * exists, and furthermore:


 * $F \left({{\varinjlim \,}_j \, C_j}\right) = {\varinjlim \,}_j \, FC_j$
 * $F p_j = q_j$


 * for all objects $j$ of $\mathbf J$.

Also see

 * Functor Creating Limits