Ext Groups for the Composition of Functors

Abstract

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.KeywordsExact SequenceSpectral SequenceShort Exact SequenceHomological AlgebraSymmetric PowerThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.