Abstract
Let M be a monoidal ∞-category with colimits. In this paper we study colimits of M-functors A → B where B is left-tensored over M and A is an M-enriched category. We prove that the enriched Yoneda embedding Y: A → PM(A) yields a universal M-functor. In case when A has a certain monoidal structure, the category of enriched presheaves PM(A) inherits the same monoidal structure and the enriched Yoneda embedding acquires the structure of universal monoidal M-functor.
| Original language | English |
|---|---|
| Pages (from-to) | 365-422 |
| Number of pages | 58 |
| Journal | Theory and Applications of Categories |
| Volume | 39 |
| Issue number | 12 |
| State | Published - 2023 |
Bibliographical note
Publisher Copyright:© Vladimir Hinich, 2023.
Keywords
- Day convolution
- enriched categories
- left-tensored categories
ASJC Scopus subject areas
- Mathematics (miscellaneous)