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arxiv: 1502.04995 · v2 · pith:E22N4OJVnew · submitted 2015-02-17 · 🧮 math.AT · math.AG

Singular chains on topological stacks

classification 🧮 math.AT math.AG
keywords topologicalsingsingularstackscategorychainsfibrationfunctor
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We extend the functor Sing of singular chains to the category of topological stacks and establish its main properties. We prove that Sing respects weak equivalences and takes a morphism of topological stacks that is both a Serre and a Reedy fibration to a Kan fibration of simplicial sets. When restricted to the category of topological spaces Sing coincides with the usual singular functor.

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