Bouc, SergeThévenaz, Jacques2020-09-082020-09-082020-09-08202110.1090/ert/564https://infoscience.epfl.ch/handle/20.500.14299/171463arXiv:1902.09816v1A 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. We determine exactly which simple correspondence functors are projective. We also determine which simple modules are projective for the algebra of all relations on a finite set. Moreover, we analyze the occurrence of such simple projective functors inside the correspondence functor F associated with a finite lattice and we deduce a direct sum decomposition of F.finite setcorrespondencefunctor categorysimple functorposetlatticetext::journal::journal article::research article