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 occuring in topology such as Segal'\''s category $ \Gamma$ , or the total category of a crossed simplicial group such as Connes'\'' cyclic category $ \Lambda$ . For any generalized Reedy category $ \RR$ and any cofibrantly generated model category $ \EE$ , the functor category $ \EE^\RR$ is shown to carry a canonical model structure of Reedy type.