Reedy categories which encode the notion of category actions

• Autorzy: Julia E. Bergner , Philip Hackney
• Języki publikacji: EN

Abstrakty

EN

We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard group actions on categories and on operads.

Kategorie tematyczne

• 18G55: Homotopical algebra
• 55U10: Simplicial sets and complexes
• 22F05: General theory of group and pseudogroup actions
• 20J99: None of the above, but in this section
• 18G30: Simplicial sets, simplicial objects (in a category)
• 55P48: Loop space machines, operads
• 18D50: Operads

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 228
• Numer: 3
• Strony: 193-222

Daty

wydano

2015

Twórcy

autor

Julia E. Bergner

• Department of Mathematics, University of California, Riverside, Riverside, CA 92521, U.S.A.

autor

Philip Hackney

• Department of Mathematics, University of California, Riverside, Riverside, CA 92521, U.S.A.

Identyfikatory

DOI

10.4064/fm228-3-1