English

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}
}