Colimits in enriched ∞-categories and Day convolution

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.

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