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Abstract: Let F (correspondingly P) denote the abelian category of functors (strict polynomial functors in the sense of Friedlander and Suslin) from finite dimensional vector spaces over Fp

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Abstract: Let F (correspondingly P) denote the abelian category of functors (strict polynomial functors in the sense of Friedlander and Suslin) from finite dimensional vector spaces over Fpto vector spaces over Fp. These two categories are related via the exact forgetful functor

ι : P → F .

The category F is strongly related to topology and representation theory of symmetric and general linear groups but the homological algebra in F is rather mysterious. The category P is easier for cohomological calculations.

The known ExtF(., .) calculations are obtained only for functors which be- long to the image of ι and are performed using comparison of ExtP- and ExtF-groups induced by ι. In my talk I am going to overview the categories F and P and their relation to concepts from algebraic topology. The aim of the talk is to present cohomological conditions which guarantee that a given functor F ∈ F comes from P via ι.

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