Representability theorems, up to homotopy

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1363-1372
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - 2020

Bibliographical note

Funding Information:
Received by the editors March 12, 2019, and, in revised form, July 24, 2019. 2010 Mathematics Subject Classification. Primary 55U35; Secondary 55P91, 18G55. Key words and phrases. Mapping spaces, representable functors, Bousfield localization, non-cofibrantly generated, model category. The research of the first author was partially supported by ISF grant 770/16. The research of the second author was partially supported by ISF grant 1138/16.

Publisher Copyright:
© 2019 American Mathematical Society.


  • Bousfield localization
  • Mapping spaces
  • Model category
  • Noncofibrantly generated
  • Representable functors

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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