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topological homotopy type is cohesive shape of continuous diffeology -- proposition

Proposition

(topological homotopy type is cohesive shape of continuous diffeology)
For every XX \in TopologicalSpaces, the cohesive shape/path ∞-groupoid presented by its diffeological singular simplicial set (Def. , Remark ) of its continuous diffeology is naturally\,weak homotopy equivalent to the homotopy type of XX presented by the ordinary singular simplicial set:

Sing diff(Cdfflg(X))W whSing(X). Sing_{diff} \big( Cdfflg(X) \big) \underoverset { \in \mathrm{W}_{wh} } {} {\longrightarrow} Sing(X) \,.

(Christensen & Wu 2013, Prop. 4.14)

Last revised on October 1, 2021 at 12:32:14. See the history of this page for a list of all contributions to it.