On an extension of the notion of Reedy category

Abstract

We extend the classical notion of a Reedy category so as to allow non-trivial automorphisms. Our extension includes many important examples occurring in topology such as Segal's category Γ, or the total category of a crossed simplicial group such as Connes' cyclic category Λ. For any generalized Reedy category ℝ and any cofibrantly generated model category ε, the functor category εℝ is shown to carry a canonical model structure of Reedy type. © 2010 The Author(s).