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

###### Proposition

(topological homotopy type is cohesive shape of continuous diffeology)
For every $X \in$ 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 $X$ presented by the ordinary singular simplicial set:

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

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