Homotopy properties of infinity-simplicial coalgebras and homotopy unital supplemented A(infinity)-algebras

摘要

The homotopy theory of infinity-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(infinity)-algebra.