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A Handbook of Model CategoriesNew Models from Old Ones

A Handbook of Model Categories: New Models from Old Ones [Suppose we have a category C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}$$\end{document} along with a choice of three classes of morphisms that we want to say form the weak equivalences, fibrations, and cofibrations of a model structure on C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}$$\end{document}. It can sometimes be tedious to check if the model categorical axioms hold or not. As such, one usually relies on general methods for forming new model structures from old ones, either on the same or on a different underlying category.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Handbook of Model CategoriesNew Models from Old Ones

Part of the Algebra and Applications Book Series (volume 27)
Balchin, Scott
A Handbook of Model Categories — Oct 30, 2021
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47 pages

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2021
ISBN
978-3-030-75034-3
Pages
41 –88
DOI
10.1007/978-3-030-75035-0_4
Publisher site
See Chapter on Publisher Site

Abstract

[Suppose we have a category C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}$$\end{document} along with a choice of three classes of morphisms that we want to say form the weak equivalences, fibrations, and cofibrations of a model structure on C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}$$\end{document}. It can sometimes be tedious to check if the model categorical axioms hold or not. As such, one usually relies on general methods for forming new model structures from old ones, either on the same or on a different underlying category.]

Published: Oct 30, 2021

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