Yoneda lemma for enriched ∞-categories

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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 languageEnglish
Article number107129
JournalAdvances in Mathematics
StatePublished - 24 Jun 2020

Bibliographical note

Publisher Copyright:
© 2020


  • Enriched infinity categories
  • Yoneda lemma

ASJC Scopus subject areas

  • General Mathematics


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