## Algebraic & Geometric Topology

### Duality and small functors

#### Abstract

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

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

Dates
Revised: 11 December 2014
Accepted: 15 December 2014
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841027

Digital Object Identifier
doi:10.2140/agt.2015.15.2609

Mathematical Reviews number (MathSciNet)
MR3426688

Zentralblatt MATH identifier
1331.18022

Subjects
Secondary: 18G55: Homotopical algebra 18A25: Functor categories, comma categories

Keywords
small functors duality

#### Citation

Biedermann, Georg; Chorny, Boris. Duality and small functors. Algebr. Geom. Topol. 15 (2015), no. 5, 2609--2657. doi:10.2140/agt.2015.15.2609. https://projecteuclid.org/euclid.agt/1510841027

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