Generalized correspondence functors

JOURNAL OF ALGEBRA

卷:521

Article

Guillaume, Clement¹ 

[1] Univ Picardie Jules Verne, CNRS, UMR 7352, Lab Amienois Math Fondamentale & Appl, 33 Rue St Leu, F-80039 Amiens 1, France

关键词: Generalized correspondence;    Lattice;    Presheaf;    Functor category;    Simple functor;    Finite length;    Dimension zero category;    Stabilization;   

DOI  :  10.1016/j.jalgebra.2018.11.036

来源: Elsevier

【 摘 要 】

A generalized correspondence functor is a functor from the category of finite sets and T-generalized correspondences to the category of all k-modules, where T is a finite distributive lattice and k a commutative ring. We parametrize simple generalized correspondence functors using the notions of T-module and presheaf of posets. As an application, we prove finiteness and stabilization results. In particular, when k is a field, any finitely generated correspondence functor has finite length, and when k is noetherian, any subfunctor of a finitely generated functor is finitely generated. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free