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 $\mathbf J$ :


 * 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 $\mathbf J$.

Also see

 * Definition:Functor Creating Limits