Duality and small functors

Georg Biedermann, Boris Chorny

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)2609-2657
Number of pages49
JournalAlgebraic and Geometric Topology
Issue number5
StatePublished - 12 Nov 2015

Bibliographical note

Publisher Copyright:
© 2015, Mathematical Sciences Publishers. All rights reserved.


  • Duality
  • Small functors

ASJC Scopus subject areas

  • Geometry and Topology


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