On the homotopy structure of strongly homotopy associative algebras (Q1295673)

Let \({\mathcal S}{\mathcal H}{\mathcal A}\) be the category of strongly homotopy associative algebras and strongly homotopy multiplicative maps. This category was first considered by \textit{J. D. Stasheff} [Trans. Am. Math. Soc. 108, 275-292, 293-312 (1963; Zbl 0114.39402)] for the study of singular chain complexes of loop spaces. The author investigates the homotopy structure of the category \({\mathcal S}{\mathcal H}{\mathcal A}\). In particular, he shows that the cocylinder functor of \({\mathcal D}{\mathcal H}{\mathcal A}\) is extended to \({\mathcal S}{\mathcal H}{\mathcal A}\) and that homotopy pullbacks exist in \({\mathcal S}{\mathcal H}{\mathcal A}\).