a) Similar construction works in the case of an arbitrary non-unital $A_{\infty}$-category. In that case one needs projectors $\Pi_{X,Y}$ and homotopies $H_{X,Y}$ for every graded space of morphisms $Hom(X,Y)$. All formulas remain the same as in the case of $A_{\infty}$-algebras. The resulting $A_{\infty}$-category with the spaces of morphisms given by $\Pi_{X,Y}(Hom(X,Y))$ is equivalent to the original one. We will use this fact later.

b) Propositions 4 and 5 should hold in a much more general case of algebras over operads (see e.g. [M]).