# A Handbook of Model CategoriesSimplicial Sets

A Handbook of Model Categories: Simplicial Sets [In this chapter we will investigate various models on the category of simplicial sets. In Part I we have already encountered two fundamental model structures, namely the Kan–Quillen model structure and the Joyal model structure. The former plays a crucial role in the formation of the homotopy function complexes that we explored in §2.5, while we saw that the latter is a convenient framework for (∞,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\infty ,1)$$\end{document}-categories in Section 5.1.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Handbook of Model CategoriesSimplicial Sets

Part of the Algebra and Applications Book Series (volume 27)
29 pages

/lp/springer-journals/a-handbook-of-model-categories-simplicial-sets-q5Dk803gFv
Publisher
Springer International Publishing
© Springer Nature Switzerland AG 2021
ISBN
978-3-030-75034-3
Pages
101 –130
DOI
10.1007/978-3-030-75035-0_6
Publisher site
See Chapter on Publisher Site

### Abstract

[In this chapter we will investigate various models on the category of simplicial sets. In Part I we have already encountered two fundamental model structures, namely the Kan–Quillen model structure and the Joyal model structure. The former plays a crucial role in the formation of the homotopy function complexes that we explored in §2.5, while we saw that the latter is a convenient framework for (∞,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\infty ,1)$$\end{document}-categories in Section 5.1.]

Published: Oct 30, 2021