Yoneda lemma for enriched ∞-categories

Vladimir Hinich

doi:10.1016/j.aim.2020.107129

Yoneda lemma for enriched ∞-categories

Vladimir Hinich

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	107129
Journal	Advances in Mathematics
Volume	367
DOIs	https://doi.org/10.1016/j.aim.2020.107129
State	Published - 24 Jun 2020

Bibliographical note

Funding Information:
A part of this work was done during the author's stay at Radboud University at Nijmegen, Utrecht University, MPIM and UC Berkeley. The author is very grateful to these institutions for the excellent working conditions. Numerous discussions with Ieke Moerdijk were very helpful. John Francis' advice for a proof of Proposition 3.6.7 is appreciated. We are very grateful to R. Haugseng who pointed out an error in the first version of the manuscript. We are also very grateful to the anonymous referee who has made an incredible job trying to make the manuscript better. The work was supported by ISF 446/15 and 786/19 grants.

Funding Information:
A part of this work was done during the author's stay at Radboud University at Nijmegen, Utrecht University, MPIM and UC Berkeley. The author is very grateful to these institutions for the excellent working conditions. Numerous discussions with Ieke Moerdijk were very helpful. John Francis' advice for a proof of Proposition 3.6.7 is appreciated. We are very grateful to R. Haugseng who pointed out an error in the first version of the manuscript. We are also very grateful to the anonymous referee who has made an incredible job trying to make the manuscript better. The work was supported by ISF 446/15 and 786/19 grants.

Publisher Copyright:
© 2020

Keywords

Enriched infinity categories
Yoneda lemma

ASJC Scopus subject areas

Mathematics (all)

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10.1016/j.aim.2020.107129

Cite this

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Yoneda lemma for enriched ∞-categories

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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