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 | English |
|---|---|
| Pages (from-to) | 1363-1372 |
| Number of pages | 10 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 148 |
| Issue number | 3 |
| DOIs | |
| State | Published - 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.
Keywords
- Bousfield localization
- Mapping spaces
- Model category
- Noncofibrantly generated
- Representable functors
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics