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

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

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