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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Left-determined model categories and universal homotopy theories


Authors: J. Rosicky and W. Tholen
Journal: Trans. Amer. Math. Soc. 355 (2003), 3611-3623
MSC (2000): Primary 55U35
Published electronically: May 15, 2003
Erratum: Trans. Amer. Math. Soc. 360 (2008), 6179-6180
MathSciNet review: 1990164
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Abstract | References | Similar Articles | Additional Information

Abstract: We say that a model category is left-determined if the weak equivalences are generated (in a sense specified below) by the cofibrations. While the model category of simplicial sets is not left-determined, we show that its non-oriented variant, the category of symmetric simplicial sets (in the sense of Lawvere and Grandis) carries a natural left-determined model category structure. This is used to give another and, as we believe simpler, proof of a recent result of D. Dugger about universal homotopy theories.


References [Enhancements On Off] (What's this?)

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Additional Information

J. Rosicky
Affiliation: Department of Mathematics, Masaryk University, 662 95 Brno, Czech Republic
Email: rosicky@math.muni.cz

W. Tholen
Affiliation: Department of Mathematics and Statistics, York University, Toronto M3J 1P3, Canada
Email: tholen@pascal.math.yorku.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03322-1
PII: S 0002-9947(03)03322-1
Received by editor(s): June 1, 2002
Published electronically: May 15, 2003
Additional Notes: The first author was supported by the Grant Agency of the Czech Republic under Grant 201/99/0310. The hospitality of the York University is gratefully acknowledged.
The second author was supported by the Natural Sciences and Engineering Council of Canada
Article copyright: © Copyright 2003 American Mathematical Society