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Colimits in enriched ∞-categories and Day convolution
Theory and applications of categories, Tome 39 (2023), pp. 365-422 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 18D20, 18N60, 18N70
Keywords: enriched categories, Day convolution, left-tensored categories 
@article{TAC_2023_39_a11,
     author = {Vladimir Hinich},
     title = {Colimits in enriched \ensuremath{\infty}-categories  and {Day} convolution},
     journal = {Theory and applications of categories},
     pages = {365--422},
     year = {2023},
     volume = {39},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a11/}
}
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Vladimir Hinich. Colimits in enriched ∞-categories  and Day convolution. Theory and applications of categories, Tome 39 (2023), pp. 365-422. http://geodesic.mathdoc.fr/item/TAC_2023_39_a11/