TY - JOUR
T1 - Taylor towers for functors of additive categories
AU - Johnson, Brenda
AU - McCarthy, Randy
N1 - Funding Information:
work was supported by National Science Foundation
PY - 1999/4/30
Y1 - 1999/4/30
N2 - 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).
AB - 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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U2 - 10.1016/S0022-4049(97)00203-X
DO - 10.1016/S0022-4049(97)00203-X
M3 - Article
AN - SCOPUS:0033617053
SN - 0022-4049
VL - 137
SP - 253
EP - 284
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 3
ER -