Yoneda lemma for enriched ∞-categories

By V. Hinich. Advances in Mathematics, 2020

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Abstract We continue the study of enriched ∞-categories, using a definition equivalent to that of Gepner and Haugseng. In our approach enriched ∞-categories are associative monoids in an especially designed monoidal category of enriched quivers. We prove that, in the case where the monoidal structure in the basic category M comes from the direct product, our definition is essentially equivalent to the approach via Segal objects. Furthermore, we compare our notion with the notion of category left-tensored over M , and prove a version of Yoneda lemma in this context. We apply the Yoneda lemma to the study of correspondences of enriched (for instance, higher) ∞-categories.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a4a086c859a7f9547468e6dd1428c69d1c8a7d23