On an extension of the notion of Reedy category

TL;DR

This paper generalizes Reedy categories to include automorphisms, enabling new applications in topology and establishing a Reedy model structure on functor categories.

Contribution

It introduces a broader class of Reedy categories with automorphisms and constructs a Reedy model structure on functor categories for these generalized categories.

Findings

Includes examples like Segal's Gamma and Connes' cyclic category Lambda

Establishes a canonical Reedy model structure on functor categories

Extends applicability of Reedy categories in topology

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 R and any cofibrantly generated model category E, the functor category E^R is shown to carry a canonical model structure of Reedy type.