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

TL;DR

This paper demonstrates the equivalence of homotopy theories of differential graded categories and A-infinity categories over a field at the $( abla,1)$-categorical level, linking different categorical frameworks.

Contribution

It establishes the $( abla,1)$-categorical equivalence between dg-categories and A-infinity categories, building on a key theorem and general relationships between various $( abla,1)$-categories.

Findings

Homotopy theories of dg-categories and A-infinity categories are equivalent.

The equivalence holds at the $( abla,1)$-categorical level.

Results rely on a theorem by Canonaco-Ornaghi-Stellari and categorical relationships.

Abstract

We show that the homotopy theories of differential graded categories and $\mathrm{A}_\infty$-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.