Operadic categories and quasi-Gr\"obner categories
Combinatorics
2023-06-09 v2 Algebraic Topology
Category Theory
Representation Theory
Abstract
Quasi-Gr\"obner categories were introduced by Sam and Snowden to unify treatment of categories in representation stability. We give new examples of quasi-Gr\"obner categories. Most of these categories are operadic categories of Batanin and Markl which are used to encode homotopy coherent structures. This suggests that other operadic categories might also be quasi-Gr\"obner. Additionally, we show that set-operads form a full subcategory of the category of operadic categories. We state several open problems.
Keywords
Cite
@article{arxiv.2205.00983,
title = {Operadic categories and quasi-Gr\"obner categories},
author = {Sergei Burkin},
journal= {arXiv preprint arXiv:2205.00983},
year = {2023}
}
Comments
Major rewrite, fixed mistakes, clarified connection between operads and operadic categories