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- W1519246809 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 $n^{text {th}}$ order approximation $P_n F$ at a space $X$ depends on the values of $F$ on coproducts of large suspensions of the space: $F(vee Sigma ^M X)$. We define an âalgebraicâ version of the Goodwillie tower, $P_n^{text {alg}} F(X)$, that depends only on the behavior of $F$ on coproducts of $X$. When $F$ is a functor to connected spaces or grouplike $H$-spaces, the functor $P_n^{text {alg}} F$ is the base of a fibration [ |{bot ^{*+1} F}| rightarrow F rightarrow P_n^{text {alg}} F, ] whose fiber is the simplicial space associated to a cotriple $bot$ built from the $(n+1)^{text {st}}$ cross effect of the functor $F$. In a range in which $F$ commutes with realizations (for instance, when $F$ 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 $F$ in many interesting cases." @default.
- W1519246809 created "2016-06-24" @default.
- W1519246809 creator A5055613304 @default.
- W1519246809 date "2005-12-20" @default.
- W1519246809 modified "2023-09-26" @default.
- W1519246809 title "Algebraic Goodwillie calculus and a cotriple model for the remainder" @default.
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- W1519246809 doi "https://doi.org/10.1090/s0002-9947-05-03936-x" @default.
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