On an extension of the notion of Reedy category
نویسندگان
چکیده
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 , or the total category of a crossed simplicial group such as Connes’ cyclic category . For any generalized Reedy category R and any cofibrantly generated model category E , the functor category ER is shown to carry a canonical model structure of Reedy type.
منابع مشابه
Reedy Categories and Their Generalizations
We observe that the Reedy model structure on a diagram category can be constructed by iterating an operation of “bigluing” model structures along a pair of functors and a natural transformation. This yields a new explanation of the definition of Reedy categories: they are almost exactly those small categories for which the category of diagrams and its model structure can be constructed by itera...
متن کاملCellular Presentations of Generalized Reedy Categories
This work in progress explores the algebraic perspective on the notion of generalized Reedy category introduced by Berger and Moerdijk [BM08]. The aim is to unify inductive arguments by means of a canonical presentation of the hom bifunctor as a “generalized cell complex.” This is analogous to the weighted (co)limits approach to ordinary Reedy category theory taken in [RV13], which inspired thi...
متن کاملInductive Presentations of Generalized Reedy Categories
This note explores the algebraic perspective on the notion of generalized Reedy category introduced by Berger and Moerdijk [BM08]. The aim is to unify inductive arguments by means of a canonical presentation of the hom bifunctor as a “generalized cell complex.” This is analogous to the weighted (co)limits approach to strict Reedy category theory presented in [RV14], which inspired this work. Th...
متن کاملA History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids
This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more general categories. Galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...
متن کاملFunctors between Reedy Model Categories of Diagrams
If D is a Reedy category and M is a model category, the category M of D-diagrams in M is a model category under the Reedy model category structure. If C → D is a Reedy functor between Reedy categories, then there is an induced functor of diagram categories M → M. Our main result is a characterization of the Reedy functors C → D that induce right or left Quillen functors M → M for every model ca...
متن کامل