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Colimits in enriched ∞-categories and Day convolution

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Vladimir Hinich

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.

Keywords:
enriched categories, Day convolution, left-tensored categories

2020 MSC:
18D20, 18N60, 18N70

*Theory and Applications of Categories,*
Vol. 39, 2023,
No. 12, pp 365-422.

Published 2023-03-21.

http://www.tac.mta.ca/tac/volumes/39/12/39-12.pdf

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