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On the construction of
functorial factorizations for model categories
Tobias Barthel and Emily Riehl |
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Algebraic & Geometric Topology 13 (2013) 1089–1124
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Abstract |
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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) –spaces and diagram spectra among others. |
Keywords
functorial factorizations, Hurewicz fibrations, algebraic
weak factorization systems
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Mathematical Subject Classification 2010
Primary: 55U35, 55U40
Secondary: 18A32, 18G55
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References |
Publication
Received: 10 May 2012
Revised: 29 November 2012
Accepted: 2 December 2012
Published: 17 April 2013
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Authors |
| Tobias Barthel | |
| Department of Mathematics Harvard University 1 Oxford Street Cambridge, MA 02138 USA |
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| Emily Riehl | |
| Department of Mathematics Harvard University 1 Oxford Street Cambridge, MA 02138 USA |
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| http://www.math.harvard.edu/~eriehl | |
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