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Left-Determined Model Categories and Universal Homotopy Theories

J. Rosický and W. Tholen
Transactions of the American Mathematical Society
Vol. 355, No. 9 (Sep., 2003), pp. 3611-3623
Stable URL: http://www.jstor.org/stable/1194855
Page Count: 13
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Left-Determined Model Categories and Universal Homotopy Theories
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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.

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