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Benjamin Briggs,
Srikanth B. Iyengar, and
Greg Stevenson
Proxy-small objects present compactly generated categories
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| Published: |
April 12, 2025. |
| Keywords: |
compactly generated triangulated category, complete intersection, small object, proxy-small object. |
| Subject [2010]: |
18G80 (primary); 13D09 (secondary). |
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Abstract
We develop a correspondence between presentations of compactly generated triangulated categories as localizations of derived categories of ring spectra and proxy-small objects, and explore some consequences. In addition, we give a characterization of proxy-smallness in terms of coproduct preservation of the associated corepresentable functor `up to base change'.
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| Acknowledgements
Briggs was partly supported by the European Union under Grant Agreement 10106455, and Iyengar was partly supported by National Science Foundation grant DMS-2001368.
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| Author information
Benjamin Briggs
Department of Mathematics
Huxley Building, South Kensington Campus
Imperial College London
London, SW7 2AZ, U.K.
b.briggs@imperial.ac.uk
Srikanth B. Iyengar
Department of Mathematics
University of Utah
Salt Lake City, UT 84112, U.S.A.
srikanth.b.iyengar@utah.edu
Greg Stevenson
Aarhus University
Department of Mathematics
Ny Munkegade 118, bldg. 1530
DK-8000 Aarhus C, Denmark
greg@math.au.dk
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