2019/09/20 by Peter Patzt, Patzt, Peter, John D. Wiltshire-Gordon +1
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1909.09729
openalex publication_date 2019/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the end-behavior of integer-valued FI-modules. Our first result describes the high degrees of an FI-module in terms of newly defined tail invariants. Our main result provides an equivalence of categories between FI-tails and finitely supported modules for a new category that we call FJ. Objects of FJ are natural numbers, and morphisms are infinite series with summands drawn from certain modules of Lie brackets.