On the Merkulov construction of $A_{ \infty}$ -(co)algebras

Abstract

UDC 512.5
The aim of this short note is to complete some aspects of a theorem proved by S. Merkulov in [Int. Math. Res. Not. IMRN. – 1999. – 3. – P. 153 – 167] (Theorem 3.4), as well as to provide a complete proof of the dual result for dg coalgebras.