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.
Original language | English |
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Pages (from-to) | 2609-2657 |
Number of pages | 49 |
Journal | Algebraic and Geometric Topology |
Volume | 15 |
Issue number | 5 |
DOIs | |
State | Published - 12 Nov 2015 |
Bibliographical note
Publisher Copyright:© 2015, Mathematical Sciences Publishers. All rights reserved.
Keywords
- Duality
- Small functors
ASJC Scopus subject areas
- Geometry and Topology