#### Volume 13, issue 2 (2013)

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On the construction of functorial factorizations for model categories

### Tobias Barthel and Emily Riehl

Algebraic & Geometric Topology 13 (2013) 1089–1124
##### 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.

##### Keywords
functorial factorizations, Hurewicz fibrations, algebraic weak factorization systems
##### Mathematical Subject Classification 2010
Primary: 55U35, 55U40
Secondary: 18A32, 18G55