Enriched Yoneda Lemma

TL;DR

This paper extends the classical Yoneda lemma to enriched categories with a focus on categories that have colimits but do not necessarily possess closed or symmetric monoidal structures.

Contribution

It introduces a version of the enriched Yoneda lemma applicable to categories with colimits, broadening the lemma's applicability beyond traditional assumptions.

Findings

The lemma applies to non-closed, non-symmetric monoidal categories.

It relaxes previous restrictions on the base monoidal category.

Provides a foundation for further research in enriched category theory.

Abstract

We present a version of enriched Yoneda lemma for conventional (not infinity-) categories. We require the base monoidal category to have colimits, but do not require it to be closed or symmetric monoidal.