Algebraic & Geometric Topology

Duality and small functors

Georg Biedermann and Boris Chorny

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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 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.

Article information

Algebr. Geom. Topol., Volume 15, Number 5 (2015), 2609-2657.

Received: 10 September 2013
Revised: 11 December 2014
Accepted: 15 December 2014
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P25: Spanier-Whitehead duality
Secondary: 18G55: Homotopical algebra 18A25: Functor categories, comma categories

small functors duality


Biedermann, Georg; Chorny, Boris. Duality and small functors. Algebr. Geom. Topol. 15 (2015), no. 5, 2609--2657. doi:10.2140/agt.2015.15.2609.

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