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
