On the construction of functorial factorizations for model categories

Barthel, Tobias¹ ; Riehl, Emily¹

¹Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 1089-1124

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.1089

Classification : 55U35, 55U40, 18A32, 18G55
Keywords: functorial factorizations, Hurewicz fibrations, algebraic weak factorization systems

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