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Proceedings of the American Mathematical Society

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Representability theorems, up to homotopy


Authors: David Blanc and Boris Chorny
Journal: Proc. Amer. Math. Soc. 148 (2020), 1363-1372
MSC (2010): Primary 55U35; Secondary 55P91, 18G55
DOI: https://doi.org/10.1090/proc/14828
Published electronically: November 13, 2019
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Abstract: We prove two representability theorems, up to homotopy, for presheaves taking values in a closed symmetric combinatorial model category $ \ensuremath {\EuScript {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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Additional Information

David Blanc
Affiliation: Department of Mathematics, University of Haifa, Haifa, Israel
Email: blanc@math.haifa.ac.il

Boris Chorny
Affiliation: Department of Mathematics, University of Haifa at Oranim, Tivon, Israel
Email: chorny@math.haifa.ac.il

DOI: https://doi.org/10.1090/proc/14828
Keywords: Mapping spaces, representable functors, Bousfield localization, non-cofibrantly generated, model category
Received by editor(s): March 12, 2019
Received by editor(s) in revised form: July 24, 2019
Published electronically: November 13, 2019
Additional Notes: 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.
Communicated by: Mark Behrens
Article copyright: © Copyright 2019 American Mathematical Society