The tensor functor from the category of $A_{\infty }$-algebras into the category of differential modules with $\infty$-simplicial faces

Abstract

The tensor functor from the category of $A_{\infty }$-algebras into the category of differential modules with $\infty$-simplicial faces is constructed. Further, it is showed that this functor sends homotopy equivalent $A_{\infty }$-algebras into homotopy equivalent differential modules with $\infty$-simplicial faces.