Duality and small functors
| Autor: | Georg Biedermann, Boris Chorny |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Pure mathematics
Functor small functors Homotopy Structure (category theory) Duality (optimization) Mathematics - Category Theory Opposite category 18G55 Mathematics::Algebraic Topology 18A25 Mathematics::K-Theory and Homology Mathematics::Category Theory FOS: Mathematics Algebraic Topology (math.AT) duality 55P25 Category Theory (math.CT) Geometry and Topology Mathematics - Algebraic Topology Mathematics |
| Zdroj: | Algebr. Geom. Topol. 15, no. 5 (2015), 2609-2657 |
| Popis: | 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 $D\colon \mathrm{Sp}\rightarrow \mathrm{Sp}^{\mathrm{op}}$ 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 $\mathrm{Sp}^{\mathrm{op}}$. In this new framework for the Spanier-Whitehead duality, $\mathrm{Sp}$ and $\mathrm{Sp}^{\mathrm{op}}$ are full subcategories of the category of small functors and dualization becomes just a fibrant replacement in our new model structure. 38 pages, final version, to appear in Algebraic and Geometric Topology |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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