Capturing Goodwillie's Derivative

David Barnes, Rosona Eldred

Research output: Contribution to journalArticle

1 Citation (Scopus)
190 Downloads (Pure)

Abstract

Recent work of Biedermann and Roendigs has translated Goodwillie's calculus of functors into the language of model categories. Their work focuses on symmetric multilinear functors and the derivative appears only briefly. In this paper we focus on understanding the derivative as a right Quillen functor to a new model category. This is directly analogous to the behaviour of Weiss's derivative in orthogonal calculus. The immediate advantage of this new category is that we obtain a streamlined and more informative proof that the n-homogeneous functors are classified by spectra with an action of the symmetric group on n objects. In a later paper we will use this new model category to give a formal comparison between the orthogonal calculus and Goodwillie's calculus of functors.
Original languageEnglish
Pages (from-to)197-222
JournalJournal of Pure and Applied Algebra
Volume220
Issue number1
Early online date19 Jun 2015
DOIs
Publication statusPublished - Jan 2016

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