Ext Groups for the Composition of Functors

In recent years we observe the growing interest in homological algebra in various categories of functors from small categories to vector spaces. Let Γ and V p be the category of finite pointed sets and the finite-dimensional vector spaces over the prime field F p respectively. The categories of functors from Γ or V p to vector spaces over F p (denoted Γ and F respectively) are of the special interest because of their relations to Steenrod algebra, stable derived functors and many other questions from algebraic topology, see for example [K], [BS], [B1], [P1] etc. Moreover the homological algebra in these categories turned out to be fairly well computable, see for example [FLS], [FFSS], [P1], [B1], [BS]. But the most general calculations of Ext F -groups obtained in [FFSS] are still not satisfactory — for the purpose of studying filtrations on Eilenberg-MacLane spaces one has to study Ext and Tor groups in categories of functors when at least one variable is given as a composition of a functor with the symmetric power.