Taylor towers for functors of additive categories

Brenda Johnson; Randy McCarthy

doi:10.1016/S0022-4049(97)00203-X

Taylor towers for functors of additive categories

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Abstract

Given a functor F : script A sign → ℬ at of additive categories, we construct a tower of functors · · · → P_nF → P_n-1F → P_n-2F → · · · → P₁F → F(0). We show that each P_nF 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).

Original language	English (US)
Pages (from-to)	253-284
Number of pages	32
Journal	Journal of Pure and Applied Algebra
Volume	137
Issue number	3
DOIs	https://doi.org/10.1016/S0022-4049(97)00203-X
State	Published - Apr 30 1999

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/S0022-4049(97)00203-X

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abstract = "Given a functor F : script A sign → ℬ at 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 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).",

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AU - McCarthy, Randy

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Taylor towers for functors of additive categories

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