New approach to the groups H*(Σn,Lien) by the homology theory of the category of functors

We study the (co)homology of a small category image with coefficients in bifunctors concentrated on two subcategories F−1(2) and F−1(0) where image is a functor. Applying obtained formulas to the category of surjections of finite sets we recover some results on the Goodwillie tower of the identity functor obtained in Arone and Mahowald, Inventiones Math. 135 (1999) 743–788 and Arone and Dwyer, Proc. London Math.Soc. 82 (2001) 229–256 and homological calculations in the theory of configuaration spaces from Cohen, J. Pure Appl. Algebra 100 (1995) 19–42 and Cohen and Taylor, Contemporary Math. 146 (1993) 91–109.