Enriched yoneda lemma

Abstract

We present a version of the enriched Yoneda lemma for conventional (not ∞-) cate-gories. We do not require the base monoidal category M to be closed or symmetric monoidal. In the case M has colimits and the monoidal structure in M preserves colimits in each argument, we prove that the Yoneda embedding A → PM(A) is a universal functor from A to a category with colimits, left-tensored over M.