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 $\Delta^{p}$ $(p \geq 0)$ such that $\Delta^{p}$ contains the $k^{th}$ horn $\Lambda^{p}_{k}$ as a smooth deformation retract.