Homological epimorphisms and homotopy epimorphisms

Abstract

We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

12 pages. In this version an erroneous definition of an acyclic map has been corrected; this has not affected the rest of the paper

Cited by in corpus (3)

• Singularity categories via the derived quotient
• Fréchet Modules and Descent
• The derived contraction algebra