A classification of small homotopy functors from spectra to spectra

Boris Chorny

doi:10.4064/fm952-12-2015

A classification of small homotopy functors from spectra to spectra

Boris Chorny

Department of Mathematics, Physics and Computer Science (Oranim Campus)

Research output: Contribution to journal › Article › peer-review

Abstract

We show that every small homotopy functor from spectra to spectra 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 spectra equipped with the homotopy model structure and the opposite of the pro-category of spectra with the strict model structure.

Original language	English
Pages (from-to)	101-125
Number of pages	25
Journal	Fundamenta Mathematicae
Volume	234
Issue number	2
DOIs	https://doi.org/10.4064/fm952-12-2015
State	Published - 2016

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2016.

Keywords

Homotopy functors
Model categories
Pro-spectra

ASJC Scopus subject areas

Algebra and Number Theory

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10.4064/fm952-12-2015

Cite this

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abstract = "We show that every small homotopy functor from spectra to spectra 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 spectra equipped with the homotopy model structure and the opposite of the pro-category of spectra with the strict model structure.",

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N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2016.

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AB - We show that every small homotopy functor from spectra to spectra 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 spectra equipped with the homotopy model structure and the opposite of the pro-category of spectra with the strict model structure.

KW - Homotopy functors

KW - Model categories

KW - Pro-spectra

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DO - 10.4064/fm952-12-2015

M3 - Article

AN - SCOPUS:84973497855

SN - 0016-2736

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JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

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ER -

A classification of small homotopy functors from spectra to spectra

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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