# Colimit functor on an enriched category

Let $$\mathscr{M}$$ be a cocomplete category enriched over topological spaces, and $$J$$ be a small (ordinary) category toplogized with the discrete topology. Is it true that the functor $$Fun(J,\mathscr{M})\rightarrow \mathscr{M}$$ taking the colimit of the diagram is a functor of categories enriched over topological spaces?