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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm952-12-2015,
author = {Boris Chorny},
title = {A classification of small homotopy functors from spectra to spectra},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {101-125},
zbl = {06602784},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm952-12-2015}
}
Boris Chorny. A classification of small homotopy functors from spectra to spectra. Fundamenta Mathematicae, Tome 233 (2016) pp. 101-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm952-12-2015/