arXiv subjects

Andrew Mauer-Oats

Publications and source records attributed to Andrew Mauer-Oats.

2 recordsLinked to original sources

arXiv2013

Goodwillie Calculi

The Goodwillie tower is based on the idea of approximating a functor F by a series of functors satisfying the strong property of "n-excision". In this dissertation, we study a weaker property of "n-additivity" and compare the two. Theorem 9.1, one of the main results in this dissertation, establishes that if $F$ is reasonably good, there is a fibration sequence with the fiber being the realization of a simplicial space built from a cotriple made of iterated cross effects and base space the "discrete" degree $n$ additive approximation to $F$. We also relate the construction given to Goodwillie's construction, and give conditions under which they coincide.

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arXiv2004

Algebraic Goodwillie calculus and a cotriple model for the remainder

We define an ``algebraic'' version of the Goodwillie tower, P_n^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^alg F is the base of a fibration whose fiber is the simplicial space associated to a cotriple built from the (n+1) cross effect of the functor F. When the connectivity of X is large enough (for example, when F is the identity functor and X is connected), 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.

math.AT↗