Correspondence functors and finiteness conditions
Representation Theory
2019-02-15 v1 Combinatorics
Category Theory
Group Theory
Abstract
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 func-tors. 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.
Cite
@article{arxiv.1902.05447,
title = {Correspondence functors and finiteness conditions},
author = {Serge Bouc and Jacques Thévenaz},
journal= {arXiv preprint arXiv:1902.05447},
year = {2019}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1510.03034