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 |
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Article number | 107129 |
Journal | Advances in Mathematics |
Volume | 367 |
DOIs | |
State | Published - 24 Jun 2020 |
Bibliographical note
Publisher Copyright:© 2020
Keywords
- Enriched infinity categories
- Yoneda lemma
ASJC Scopus subject areas
- General Mathematics