Definition:Colimit/Finite Colimit

Definition
Let $\mathbf C$ be a metacategory.

Let $D: \mathbf J \to \mathbf C$ be a $\mathbf J$-diagram in $\mathbf C$. Let $\varinjlim_j D_j$ be a colimit for $D$.

Then $\varinjlim_j D_j$ is called a finite colimit iff $\mathbf J$ is a finite category.

Also see

 * Finitely Cocomplete Category