Duality and small functors

Biedermann, Georg¹ ; Chorny, Boris²

¹LAGA – Institut Galilée, Université Paris 13, 99 avenue Jean Baptiste Clément, 93430 Villetaneuse, France
²Department of Mathematics, Physics and Computer Science, University of Haifa at Oranim, 36006 Tivon, Israel

Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2609-2657

Résumé

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 D: Sp → Spop 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 Spop. In this new framework for the Spanier–Whitehead duality, Sp and Spop are full subcategories of the category of small functors and dualization becomes just a fibrant replacement in our new model structure.

Détail

DOI : 10.2140/agt.2015.15.2609

Classification : 55P25, 18G55, 18A25
Keywords: small functors, duality

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