English

Extensions of representation stable categories

Representation Theory 2023-01-27 v2 Category Theory

Abstract

A category of FI type is one which is sufficiently similar to finite sets and injections so as to admit nice representation stability results. Several common examples admit a Grothendieck fibration to finite sets and injections. We begin by carefully reviewing the theory of fibrations of categories with motivating examples relevant to algebra and representation theory. We classify which functors between FI type categories are fibrations, and thus obtain sufficient conditions for an FI type category to be the result of a Grothendieck construction.

Keywords

Cite

@article{arxiv.2209.03879,
  title  = {Extensions of representation stable categories},
  author = {Joe Moeller},
  journal= {arXiv preprint arXiv:2209.03879},
  year   = {2023}
}

Comments

23 pages, added a "future work and open questions" section, comments welcome

R2 v1 2026-06-28T00:58:04.470Z