Correspondence functors and lattices
Representation Theory
2019-02-15 v1 Combinatorics
Category Theory
Group Theory
Abstract
A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative 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.
Cite
@article{arxiv.1902.05444,
title = {Correspondence functors and lattices},
author = {Serge Bouc and Jacques Thévenaz},
journal= {arXiv preprint arXiv:1902.05444},
year = {2019}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1510.03034