Colimits in enriched ∞-categories and Day convolution

2021/01/23 by Hinich, Vladimir
#18D20 #18N60 #18N70 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2101.09538

Abstract

For a monoidal ∞-category M with colimits, we study colimits of M-functors A\toB 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 and, in the case when A has a certain monoidal structure, the category of enriched presheaves P_M(A) inherits the same monoidal structure.

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