English

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

R2 v1 2026-06-24T11:04:54.660Z