Left-determined model categories and universal homotopy theories
Copyright policy )Left-determined model categories and universal homotopy theories
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.
- Masaryk University Czech Republic
- York University Canada
Simplicial sets and complexes in algebraic topology, cofibrations, universal model category, Abstract and axiomatic homotopy theory in algebraic topology, simplicial sets, left-determined model category, weak equivalences
Simplicial sets and complexes in algebraic topology, cofibrations, universal model category, Abstract and axiomatic homotopy theory in algebraic topology, simplicial sets, left-determined model category, weak equivalences
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