Homological epimorphisms, homotopy epimorphisms and acyclic maps
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AbstractWe 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.
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2001 ◽
Vol 27
(8)
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pp. 505-512
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2020 ◽
pp. 161-166
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