Extensions of representation stable categories
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.
 Publication:

arXiv eprints
 Pub Date:
 September 2022
 DOI:
 10.48550/arXiv.2209.03879
 arXiv:
 arXiv:2209.03879
 Bibcode:
 2022arXiv220903879M
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Category Theory;
 18D30 20C30
 EPrint:
 23 pages, added a "future work and open questions" section, comments welcome