Brown representability for space-valued functors

Details Brown representability for space-valued functors Brown representability for space-valued functors

2007-07-06

arxiv.org/abs/0707.0904v3

Mathematics

Algebraic Topology

19 pages, final version, accepted by the Israel Journal of Mathematics

Scientific paper

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 small contravariant functors from spaces to spaces up to weak equivalence of functors. In more detail, we show that every small contravariant functor from spaces to spaces which takes coproducts to products up to homotopy and takes homotopy pushouts to homotopy pullbacks is naturally weekly 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.

Affiliated with

Also associated with

No associations

Rating

Brown representability for space-valued functors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Brown representability for space-valued functors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Brown representability for space-valued functors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-90003