Reedy categories which encode the notion of category actions

Julia E. Bergner¹ ; Philip Hackney¹

¹ Department of Mathematics University of California, Riverside Riverside, CA 92521, U.S.A.

Fundamenta Mathematicae, Tome 228 (2015) no. 3, pp. 193-222

Résumé

We study a certain type of action of categories on categories and on operads. Using the structure of the categories $\Delta $ and $\Omega $ 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.

Détail

DOI : 10.4064/fm228-3-1

Keywords: study certain type action categories categories operads using structure categories delta omega governing category operad structures respectively define categories which instead encode structure category acting category category acting operad prove former has structure elegant reedy category whereas latter has structure generalized reedy category particular approach gives regard group actions categories operads