Open Access
2013 On the construction of functorial factorizations for model categories
Tobias Barthel, Emily Riehl
Algebr. Geom. Topol. 13(2): 1089-1124 (2013). DOI: 10.2140/agt.2013.13.1089


We present general techniques for constructing functorial factorizations appropriate for model structures that are not known to be cofibrantly generated. Our methods use “algebraic” characterizations of fibrations to produce factorizations that have the desired lifting properties in a completely categorical fashion. We illustrate these methods in the case of categories enriched, tensored and cotensored in spaces, proving the existence of Hurewicz-type model structures, thereby correcting an error in earlier attempts by others. Examples include the categories of (based) spaces, (based) G–spaces and diagram spectra among others.


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Tobias Barthel. Emily Riehl. "On the construction of functorial factorizations for model categories." Algebr. Geom. Topol. 13 (2) 1089 - 1124, 2013.


Received: 10 May 2012; Revised: 29 November 2012; Accepted: 2 December 2012; Published: 2013
First available in Project Euclid: 19 December 2017

zbMATH: 1268.18001
MathSciNet: MR3044604
Digital Object Identifier: 10.2140/agt.2013.13.1089

Primary: 55U35 , 55U40
Secondary: 18A32 , 18G55

Keywords: algebraic weak factorization systems , functorial factorizations , Hurewicz fibrations

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.13 • No. 2 • 2013
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