Symmetric simplicial sets
Masaryk University, Brno, Czech Republic
Coauthors: W. Tholen (York University, Toronto, Canada)
In 1988, F. W. Lawvere suggested to use the topos SetFop (where F is the category of non-empty finite sets) in algebraic topology. His suggestion was recently heard by M. Grandis who called SetFop the topos of symmetric simplicial sets and developed some homotopy theory in it. We show that the topos of symmetric simplicial sets carries a (Quillen) model structure which is Quillen equivalent to that on the topos SSet of simplicial sets. Surprisingly, the model structure of symmetric simplicial sets is determined by cofibrations only. As an application, we give a new and simpler proof of the recent result of D. Dugger about universal model categories. This result roughly says that every model category is an image of SSet. Since model categories form the foundation of homotopy theory, a universal homotopy category means a universal homotopy theory.
Date received: February 28, 2001
Copyright © 2001 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cafw-43.