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ISSN (electronic): 1472-2739
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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

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.

functorial factorizations, Hurewicz fibrations, algebraic weak factorization systems
Mathematical Subject Classification 2010
Primary: 55U35, 55U40
Secondary: 18A32, 18G55
Received: 10 May 2012
Revised: 29 November 2012
Accepted: 2 December 2012
Published: 17 April 2013
Tobias Barthel
Department of Mathematics
Harvard University
1 Oxford Street
Cambridge, MA 02138
Emily Riehl
Department of Mathematics
Harvard University
1 Oxford Street
Cambridge, MA 02138