A classification of small linear functors

Topology Seminar

Speaker: Boris Chorny (University of Haifa at Oranim)

Title: A classification of small linear functors

Abstract: We extend Goodwillie’s classification of finitary linear functors to arbitrary small functors. (A functor is small if it commutes with $\lambda$-filtered colimits for some cardinal $\lambda$.) Namely we show that every small linear simplicial functor from spectra to simlpicial sets 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 simplicial sets equipped with the linear model structure and the opposite of the pro-category of spectra with the strict model structure.