Reedy categories which encode the notion of category actions
Algebraic Topology
2014-12-31 v2 Category Theory
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.
Keywords
Cite
@article{arxiv.1207.3467,
title = {Reedy categories which encode the notion of category actions},
author = {Julia E. Bergner and Philip Hackney},
journal= {arXiv preprint arXiv:1207.3467},
year = {2014}
}