## Algebraic & Geometric Topology

### On the construction of functorial factorizations for model categories

#### Abstract

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.

#### Article information

Source
Algebr. Geom. Topol., Volume 13, Number 2 (2013), 1089-1124.

Dates
Revised: 29 November 2012
Accepted: 2 December 2012
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715550

Digital Object Identifier
doi:10.2140/agt.2013.13.1089

Mathematical Reviews number (MathSciNet)
MR3044604

Zentralblatt MATH identifier
1268.18001

#### Citation

Barthel, Tobias; Riehl, Emily. On the construction of functorial factorizations for model categories. Algebr. Geom. Topol. 13 (2013), no. 2, 1089--1124. doi:10.2140/agt.2013.13.1089. https://projecteuclid.org/euclid.agt/1513715550

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