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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: 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

W. Tholen
Affiliation: Department of Mathematics and Statistics, York University, Toronto M3J 1P3, Canada

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