Correspondence functors and finiteness conditions

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties which do not hold for other types of functors....

Full description

Saved in:
Bibliographic Details
Published in:Journal of algebra 2018-02, Vol.495, p.150-198
Main Authors: Bouc, Serge, Thévenaz, Jacques
Format: Article
Language:English
Subjects:
Category Theory
Combinatorics
Correspondence
Finite length
Finite set
Functor category
Group Theory
Mathematics
Poset
Representation Theory
Simple functor
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties which do not hold for other types of functors. In particular, if k is a field and if F is a correspondence functor, then F is finitely generated if and only if the dimension of F(X) grows exponentially in terms of the cardinality of the finite set X. Moreover, in such a case, F has actually finite length. Also, if k is noetherian, then any subfunctor of a finitely generated functor is finitely generated.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2017.11.010