Taylor towers for functors of additive categories

Abstract

Given a functor F: A → B of additive categories, we construct a tower of functors … → P n F → P n − 1 F → P n − 2 F → … → P 1 F → F(0). We show that each P n F is degree n up to chain homotopy and, under certain assumptions, approximates F in a range that grows with n. We compare our Taylor tower with Goodwillie's Taylor tower for a functor of spaces and establish conditions under which they are equivalent. This is a continuation of work by Johnson and McCarthy (to appear).