Homology, Homotopy and Applications

Volume 26 (2024)

Number 1

Remarks on the equivalence between differential graded categories and A-infinity categories

Pages: 275 – 285

DOI: https://dx.doi.org/10.4310/HHA.2024.v26.n1.a17

Author

James Pascaleff (Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Il., U.S.A.)

Abstract

We show that the homotopy theories of differential graded categories and $A_\infty$-categories over a field are equivalent at the $(\infty, 1)$-categorical level. The results are corollaries of a theorem of Canonaco–Ornaghi–Stellari combined with general relationships between different versions of $(\infty, 1)$-categories.

Keywords

differential graded category, A-infinity category

2010 Mathematics Subject Classification

18G35

Received 15 February 2023

Received revised 16 March 2023

Accepted 5 April 2023

Published 1 May 2024