Algebraic Goodwillie calculus and a cotriple model for the remainder
Author:
Andrew MauerOats
Journal:
Trans. Amer. Math. Soc. 358 (2006), 18691895
MSC (2000):
Primary 55P65
Published electronically:
December 20, 2005
MathSciNet review:
2197433
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Abstract: Goodwillie has defined a tower of approximations for a functor from spaces to spaces that is analogous to the Taylor series of a function. His order approximation at a space depends on the values of on coproducts of large suspensions of the space: . We define an ``algebraic'' version of the Goodwillie tower, , that depends only on the behavior of on coproducts of . When is a functor to connected spaces or grouplike spaces, the functor is the base of a fibration whose fiber is the simplicial space associated to a cotriple built from the cross effect of the functor . In a range in which commutes with realizations (for instance, when is the identity functor of spaces), the algebraic Goodwillie tower agrees with the ordinary (topological) Goodwillie tower, so this theory gives a way of studying the Goodwillie approximation to a functor in many interesting cases.
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Additional Information
Andrew MauerOats
Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email:
amauer@math.northwestern.edu
DOI:
http://dx.doi.org/10.1090/S000299470503936X
PII:
S 00029947(05)03936X
Received by editor(s):
December 9, 2002
Published electronically:
December 20, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
