Lifting functors from to

Abstract

Abstract Let (correspondingly ) denote the abelian category of functors (strict polynomial functors in the sense of Friedlander and Suslin) from finite dimensional vector spaces over Fp to vector spaces over Fp . These two categories are related via the exact forgetful functor The category is strongly related to topology and representation theory of symmetric and general linear groups but the homological algebra in is rather mysterious. The category is easier for cohomological calculations. The known calculations are obtained only for functors which belong to the image of ι and are performed using comparison of - and -groups induced by ι. The aim of the following note is to find cohomological conditions which guarantee that a given functor comes from via ι.