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.

中文翻译：

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同伦表同态、同伦表态和无环映射

摘要 我们证明了微分分级代数范畴中同伦表同态和同调表态的概念是等价的。作为一个应用，我们根据基于循环空间的链代数的诱导映射获得拓扑空间的非循环映射的表征。在通用非循环地图的情况下，我们获得了针对大类空间的这些诱导地图在派生定位方面的显式代数描述。