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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-3-1,
author = {Julia E. Bergner and Philip Hackney},
title = {Reedy categories which encode the notion of category actions},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {193-222},
zbl = {1314.55007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-3-1}
}
Julia E. Bergner; Philip Hackney. Reedy categories which encode the notion of category actions. Fundamenta Mathematicae, Tome 228 (2015) pp. 193-222. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-3-1/