The homotopy theory of equivariant posets

Abstract

Let $G$ be a discrete group. We prove that the category of $G$-posets admits a model structure that is Quillen equivalent to the standard model structure on $G$-spaces. As is already true nonequivariantly, the three classes of maps defining the model structure are not well understood calculationally. To illustrate, we exhibit some examples of cofibrant and fibrant posets and an example of a non-cofibrant finite poset.

22 pages; minor improvements suggested by the referee, final version, to appear in Cahiers de Topologie et Géométrie Différentielle Catégoriques

References in corpus (1)

• Cofibrant objects in the Thomason Model Structure

Cited by in corpus (3)

• Elmendorf constructions for $G$-categories and $G$-posets
• Categorical models of unstable G-global homotopy theory
• Fiber bundles over Alexandroff spaces