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The Quillen model structure on the category of diffeological spaces

Tadayuki Haraguchi, Kazuhisa Shimakawa

Abstract

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

The Quillen model structure on the category of 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.

Paper Structure

This paper contains 6 sections, 28 theorems, 48 equations.

Table of Contents

  1. Introduction
  2. Diffeological spaces and Homotopy sets
  3. Tame maps and approximate retractions
  4. Fibrations
  5. Model category of diffeological spaces
  6. Infinite gluing construction

Key Result

Theorem 2.1

The following hold:

Theorems & Definitions (53)

  • Theorem 2.1
  • Proposition 2.2
  • proof
  • Definition 2.3
  • Proposition 2.4
  • Proposition 2.5
  • proof
  • Corollary 2.6
  • Definition 2.7
  • Proposition 2.8
  • ...and 43 more