New approach to the groups [formula omitted] by the homology theory of the category of functors

Abstract

We study the (co)homology of a small category C with coefficients in bifunctors concentrated on two subcategories F −1(2) and F −1(0) where F: C→{0<1<2} 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.