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.
Bibliographical noteFunding 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.
© 2019 American Mathematical Society.
- Bousfield localization
- Mapping spaces
- Model category
- Noncofibrantly generated
- Representable functors
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics