부산대학교 도서관

We study functors F from C_f to D where C and D are simplicial model categories and C_f is the full subcategory of C consisting of objects that factor a fixed morphism f from A to B. We define the analogs of Eilenberg and Mac Lane's cross effects functors in this context, and identify explicit adjoint pairs of functors whose associated cotriples are the diagonals of the cross effects. With this, we generalize the cotriple Taylor tower construction of [10] from the setting of functors from pointed categories to abelian categories to that of functors from C_f to D to produce a tower of functors whose n-th term is a degree n functor. We compare this tower to Goodwillie's tower of n-excisive approximations to F found in [8]. When D is a good category of spectra, and F is a functor that commutes with realizations, the towers agree. More generally, for functors that do not commute with realizations, we show that the terms of the towers agree when evaluated at the initial object of C_f.
Comment: 55 pages. With appendix by Rosona Eldred. Submitted to Transactions of the AMS. New version adds section 7 on convergence of the cotriple tower. Second update makes repairs to section 3 in the proof of establishing the cotriple, adds a careful accounting of homotopy (co)limit properties being used in the paper, some of these are established in a new appendix