Colimits in enriched ∞-categories and Day convolution

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 -> P_M(A) yields a universal M-functor. In case when A has a certain monoidal str...

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Bibliographic Details
Published in:Theory and applications of categories 2023-01, Vol.39 (22), p.365
Main Author: Hinich, Vladimir
Format: Article
Language:English
Subjects:
Algebraic group theory
Classification
Embedding
Enrichment
Theoretical mathematics
Online Access:Get full text
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Summary: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 -> P_M(A) yields a universal M-functor. In case when A has a certain monoidal structure, the category of enriched presheaves P_M(A) inherits the same monoidal structure and the enriched Yoneda embedding acquires the structure of universal monoidal M-functor.
ISSN:1201-561X