The Quillen model structure on the category of diffeological spaces

TL;DR

This paper develops a Quillen model structure on the category of diffeological spaces, establishing a framework for smooth homotopy theory with weak equivalences defined by smooth weak homotopy equivalences.

Contribution

It introduces a novel model structure on diffeological spaces that facilitates homotopical analysis using smooth weak homotopy equivalences.

Findings

Established a Quillen model structure on diffeological spaces

Defined weak equivalences as smooth weak homotopy equivalences

Provided a foundation for smooth homotopy theory in diffeological spaces

Abstract

We construct on the category of diffeological spaces a Quillen model structure having smooth weak homotopy equivalences as the class of weak equivalences.