A Classification of Small Linear Functors

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Abstract

We extend Goodwillie's classification of finitary linear functors to arbitrary small functors. That is we show that every small linear simplicial functor from spectra to pointed simplicial sets is weakly equivalent to a filtered colimit of representable functors represented in cofibrant spectra. Moreover, we present this classification as a Quillen equivalence of the category of small functors from spectra to simplicial sets equipped with the linear model structure and the opposite of the pro-category of spectra with the strict model structure.

Original languageEnglish
Pages (from-to)5493-5517
Number of pages25
JournalInternational Mathematics Research Notices
Volume2016
Issue number18
DOIs
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2015 The Author(s) 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

ASJC Scopus subject areas

  • General Mathematics

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