Fibrations of simplicial sets

Details Fibrations of simplicial sets Fibrations of simplicial sets

2008-10-28

arxiv.org/abs/0810.4960v1

Mathematics

Category Theory

11 pages; to appear in Applied Categorical Structures

Scientific paper

There are infinitely many variants of the notion of Kan fibration that, together with suitable choices of cofibrations and the usual notion of weak equivalence of simplicial sets, satisfy Quillen's axioms for a homotopy model category. The combinatorics underlying these fibrations is purely finitary and seems interesting both for its own sake and for its interaction with homotopy types. To show that these notions of fibration are indeed distinct, one needs to understand how iterates of Kan's Ex functor act on graphs and on nerves of small categories.

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