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Duality and small
functors
Georg Biedermann and Boris Chorny |
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Algebraic & Geometric Topology 15 (2015) 2609–2657
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Abstract |
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The homotopy theory of small functors is a useful tool for studying various questions in homotopy theory. In this paper, we develop the homotopy theory of small functors from spectra to spectra, and study its interplay with Spanier–Whitehead duality and enriched representability in the dual category of spectra. We note that the Spanier–Whitehead duality functor factors through the category of small functors from spectra to spectra, and construct a new model structure on the category of small functors, which is Quillen equivalent to . In this new framework for the Spanier–Whitehead duality, and are full subcategories of the category of small functors and dualization becomes just a fibrant replacement in our new model structure. |
Keywords
small functors, duality
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Mathematical Subject Classification 2010
Primary: 55P25
Secondary: 18G55, 18A25
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References |
Publication
Received: 10 September 2013
Revised: 11 December 2014
Accepted: 15 December 2014
Published: 10 December 2015
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Authors |
| Georg Biedermann | |
| LAGA – Institut Galilée Université Paris 13 99 avenue Jean Baptiste Clément 93430 Villetaneuse France |
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| http://www.math.sciences.univ-nantes.fr/~biedermann/ | |
| Boris Chorny | |
| Department of Mathematics, Physics
and Computer Science University of Haifa at Oranim 36006 Tivon Israel |
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| http://math.haifa.ac.il/chorny/ | |
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