naa a22 4500 510783538 CHVBK 20180411083255.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11856-012-0063-7 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0063-7 Chorny Boris Department of Mathematics, The University of Haifa at Oranim, 36006, Tivon, Israel aut Brown representability for space-valued functors [Elektronische Daten] [Boris Chorny] In this paper we prove two theorems which resemble the classical cohomological and homological Brown representability theorems. The main difference is that our results classify contravariant functors from spaces to spaces up to weak equivalence of functors. In more detail, we show that every contravariant functor from spaces to spaces which takes coproducts to products up to homotopy, and takes homotopy pushouts to homotopy pullbacks is naturally weakly equivalent to a representable functor. The second representability theorem states: every contravariant continuous functor from the category of finite simplicial sets to simplicial sets taking homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a representable functor. This theorem may be considered as a contravariant analog of Goodwillie's classification of linear functors [14]. Hebrew University Magnes Press, 2012 Israel Journal of Mathematics Springer US; http://www.springer-ny.com 194/2(2013-03-01), 767-791 0021-2172 194:2<767 2013 194 11856 https://doi.org/10.1007/s11856-012-0063-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0063-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chorny Boris Department of Mathematics, The University of Haifa at Oranim, 36006, Tivon, Israel aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 194/2(2013-03-01), 767-791 0021-2172 194:2<767 2013 194 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer