On the construction of functorial factorizations for model categories

Tobias Barthel, Emily Riehl

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1089-1124
Number of pages36
JournalAlgebraic and Geometric Topology
Issue number2
Publication statusPublished - 17 Apr 2013
Externally publishedYes


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