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

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.