Homological perturbation theory and associativity
Pedro Real
January 1997.

Abstract:
In this paper, we prove various results concerning DGA-algebras and 
DGA-coalgebras in the context of the Homological Perturbation Theory.
More precisely, we establish here a perturbation machinery that is a
generalization of the Algebra Perturbation Lemma of [11] and [15]. We 
show three important cases in which these results are essential for
the construction of algebra or coalgebra structures in various chain
complexes.