Deriving calculus with cotriples

B. Johnson, R. McCarthy

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a Taylor tower for functors from pointed categories to abelian categories via cotriples associated to cross effect functors. The tower was inspired by Goodwillie's Taylor tower for functors of spaces, and is related to Dold and Puppe's stable derived functors and Mac Lane's Q-construction. We study the layers, D nF = fiber(P nF → P n-1F), and the limit of the tower, For the latter we determine a condition on the cross effects that guarantees convergence. We define differentials for functors, and establish chain and product rules for them. We conclude by studying exponential functors in this setting and describing their Taylor towers.

Original languageEnglish (US)
Pages (from-to)757-803
Number of pages47
JournalTransactions of the American Mathematical Society
Volume356
Issue number2
DOIs
StatePublished - Feb 2004

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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