Homotopy properties of ∞-simplicial coalgebras and homotopy unital supplemented A∞-algebras

Abstract

The homotopy theory of ∞-simplicial coalgebras is developed; in terms of this theory, an additional structure on the tensor bigraded coalgebra of a graded module is described such that endowing the coalgebra with this structure is equivalent to endowing the given graded module with the structure of a homotopy unital A_∞-algebra.