  For a monoidal $\infty$-category $\mathcal{M}$ with colimits, we study
colimits of $\mathcal{M}$-functors $\mathcal{A}\to\mathcal{B}$ where
$\mathcal{B}$ is left-tensored over $\mathcal{M}$ and $\mathcal{A}$ is an
$\mathcal{M}$-enriched category. We prove that the enriched Yoneda embedding
$Y:\mathcal{A}\to P_{\mathcal{M}}(\mathcal{A})$ yields a universal
$\mathcal{M}$-functor and, in the case when $\mathcal{A}$ has a certain
monoidal structure, the category of enriched presheaves
$P_{\mathcal{M}}(\mathcal{A})$ inherits the same monoidal structure.
