Homology, Homotopy and Applications

Volume 23 (2021)

Number 1

The operad that co-represents enrichment

Pages: 387 – 401

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n1.a20


Andrew W. Macpherson (Yokosuka-shi, Japan)


I show that the theories of enrichment in a monoidal infinity-category defined by Hinich and by Gepner–Haugseng agree, and that the identification is unique. Among other things, this makes the Yoneda lemma available in the latter model.


enriched higher category, planar operad, simplicial multicategory

This work was supported in part by World Premier International Research Center Initiative (WPI), MEXT, Japan, and in part by JSPS KAKENHI Grant Number JP19K14522.

Received 30 January 2020

Received revised 22 May 2020

Accepted 9 August 2020

Published 9 December 2020