Extensions of representation stable categories
Joe Moeller
TL;DR
This paper explores the structure of FI type categories, focusing on fibrations and Grothendieck constructions, to advance understanding of their representation stability properties.
Contribution
It classifies fibrations between FI type categories and provides conditions under which these categories arise from Grothendieck constructions.
Findings
Classification of fibrations between FI type categories
Conditions for categories to be obtained via Grothendieck construction
Enhanced understanding of representation stability in algebraic contexts
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology