Model category of diffeological spaces

Abstract

The existence of a model structure on the category $\mathcal{D}$ of diffeological spaces is crucial to developing smooth homotopy theory. We construct a compactly generated model structure on the category $\mathcal{D}$ whose weak equivalences are just smooth maps inducing isomorphisms on smooth homotopy groups. The essential part of our construction of the model structure on $\mathcal{D}$ is to introduce diffeologies on the sets ${\Delta }^p$ $(p\ge 0)$ such that ${\Delta }^p$ contains the $k^{th}$ horn ${\Lambda }_k^p$ as a smooth deformation retract.

Main points of modification: Axiom 3 for the standard simplices is weakened. However, new Axiom 3 is equivalent to old Axiom 3 under the presence of Axiom 2 (Lemma 9.2)

References in corpus (1)

• The D-topology for diffeological spaces

Cited by in corpus (2)

• Smooth constructions of homotopy-coherent actions
• Towards Riemannian diffeology