Representability theorems, up to homotopy

David Blanc; Boris Chorny

doi:10.1090/proc/14828

Representability theorems, up to homotopy

David Blanc, Boris Chorny

University of Haifa

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

Abstract

We prove two representability theorems, up to homotopy, for presheaves taking values in a closed symmetric combinatorial model category V. The first theorem resembles the Freyd representability theorem, and the second theorem is closer to the Brown representability theorem. As an application we discuss a recognition principle for mapping spaces.

Original language	American English
Pages (from-to)	1363-1372
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	3
DOIs	https://doi.org/10.1090/proc/14828
State	Published - 2020

Keywords

Bousfield localization
Mapping spaces
Model category
Noncofibrantly generated
Representable functors

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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10.1090/proc/14828

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title = "Representability theorems, up to homotopy",

abstract = "We prove two representability theorems, up to homotopy, for presheaves taking values in a closed symmetric combinatorial model category V. The first theorem resembles the Freyd representability theorem, and the second theorem is closer to the Brown representability theorem. As an application we discuss a recognition principle for mapping spaces.",

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AU - Blanc, David

AU - Chorny, Boris

PY - 2020

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AB - We prove two representability theorems, up to homotopy, for presheaves taking values in a closed symmetric combinatorial model category V. The first theorem resembles the Freyd representability theorem, and the second theorem is closer to the Brown representability theorem. As an application we discuss a recognition principle for mapping spaces.

KW - Bousfield localization

KW - Mapping spaces

KW - Model category

KW - Noncofibrantly generated

KW - Representable functors

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U2 - 10.1090/proc/14828

DO - 10.1090/proc/14828

M3 - Article

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EP - 1372

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

Representability theorems, up to homotopy

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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