Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896518 | Journal of Algebra | 2018 | 49 Pages |
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 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Serge Bouc, Jacques Thévenaz,