Bouc, SergeThévenaz, Jacques2017-11-172017-11-172017-11-17201810.1016/j.jalgebra.2017.11.010https://infoscience.epfl.ch/handle/20.500.14299/142201WOS:000418106900007We 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.Finite setCorrespondenceFunctor categorySimple functorFinite lengthPosettext::journal::journal article::research article