Reedy categories which encode the notion of category actions
Volume 228 / 2015
Fundamenta Mathematicae 228 (2015), 193-222
MSC: Primary 55P48; Secondary 20J99, 22F05, 55U10, 18D50, 18G30, 18G55.
DOI: 10.4064/fm228-3-1
Abstract
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.
