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

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