Sous-objets deI circle times operator Λndans la catégorie des foncteurs entre image2-espaces vectoriels Original Research Article

Let image denote the abelian category of functors from finite-dimensional image2-vector spaces to image2-vector spaces. We are concerned with the artinian conjecture, which states that the injective functorsIEare artinian objects in image for each finite dimensional image2-vector spaceE. This is true for dim E = 1 and has been recently proven for dim E = 2. This paper gives one of the arguments of this proof: we produce a sequence of objects of image,image, whose subobjects are finite in a sense that generalizes the case dim E = 1. The main ingredients are the behaviour of the difference functor on Weyl functors and simple functors, and the computation of some extension groups.