Souriau introduced diffeological spaces as a generalization of the notion of smooth manifolds in 1980. We know that the category of diffeological spaces is complete, cocomplete and cartesian closed. In this talk, I introduce the notion of smooth cell complexes which are constructed inductively by a process of attaching $n$-cubes $I^{n}$ along their boundary $\partial I^{n}$, and give a method to discuss smooth homotopy theory of diffeological spaces. The purpose of this talk is to introduce the results and techniques related to the homotopy extension property of smooth cell complexes.

This talk is based on a joint work with Kazuhisa Shimakawa (Okayama University).