Taylor towers for functors of additive categories Original Research Article

Given a functor image of additive categories, we construct a tower of functors … → PnF → Pn − 1F → Pn − 2F → … → P1F → F(0). We show that each PnF 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 Goodwillieʹs 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).