2008/09/19 by Clemens Berger, Ieke Moerdijk
Mathematics · #Algebraic structures and combinatorial models #Category of sets #Category theory #Closed category #Concrete category #Extension (predicate logic) #Functor #Homotopy and Cohomology in Algebraic Topology #Model category #Rings, Modules, and Algebras #math.AT #math.CT #msc:18G30 #msc:18G55 #msc:20N99 #msc:55U35
paper · pdf · doi:10.1007/s00209-010-0770-x
published as Math. Z. 269 (2011), 977-1004
arxiv created 2008/09/19 · openalex publication_date 2010/09/08 · arxiv updated 2016/04/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 \mathbb R and any cofibrantly generated model category E , the functor category E^\mathbb R is shown to carry a canonical model structure of Reedy type.