We show that every small homotopy functor from spectra to spectra is weakly equivalent to a filtered colimit of representable functors represented in cofibrant spectra. Moreover, we present this classification as a Quillen equivalence of the category of small functors from spectra to spectra equipped with the homotopy model structure and the opposite of the pro-category of spectra with the strict model structure.
Bibliographical notePublisher Copyright:
© Instytut Matematyczny PAN, 2016.
- Homotopy functors
- Model categories
ASJC Scopus subject areas
- Algebra and Number Theory