Correspondence functors and duality

Serge Bouc (1) , Jacques Thévenaz (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 Section de Mathematiques [Lausanne]

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. By means of a suitably defined duality, new correspondence functors are constructed, having remarkable properties. In particular, their evaluation at any finite set is always a free k-module and an explicit formula is obtained for its rank. The results use some subtle new ingredients from the theory of finite lattices. (c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Mots clés: Finite set; Correspondence; Functor category; Simple functor; Poset; Lattice

Domaines: Mathématiques [math]

Serge Bouc, Jacques Thévenaz. Correspondence functors and duality. Journal of Algebra, 2023, 617, pp.425-475. ⟨10.1016/j.jalgebra.2022.10.028⟩. ⟨hal-04020769⟩