Correspondence functors and lattices

JOURNAL OF ALGEBRA

卷:518

Article

Bouc, Serge¹  Thevenaz, Jacques² 

[1] Univ Picardie Jules Verne, CNRS, LAMFA, 33 Rue St Leu, F-80039 Amiens 1, France

[2] Ecole Polytech Fed Lausanne, Sect Math, Stn 8, CH-1015 Lausanne, Switzerland

关键词: Finite set;    Correspondence;    Functor category;    Simple functor;    Poset;    Lattice;   

DOI  :  10.1016/j.jalgebra.2018.10.019

来源: Elsevier

【 摘 要 】

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. A main tool for this study is the construction of a correspondence functor associated to any finite lattice T. We prove for instance that this functor is projective if and only if the lattice T is distributive. Moreover, it has quotients which play a crucial role in the analysis of simple functors. The special case of total orders yields some more specific and complete results. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free