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

DOI:
https://doi.org/10.1090/S0002-9947-03-03322-1

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.

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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:
https://doi.org/10.1090/S0002-9947-03-03322-1

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