A classification of small homotopy functors from spectra to spectra
Volume 234 / 2016
Fundamenta Mathematicae 234 (2016), 101-125
MSC: Primary 18G55; Secondary 55P42.
DOI: 10.4064/fm952-12-2015
Published online: 2 March 2016
Abstract
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.
