Décalage and Kan's simplicial loop group functor

Details Décalage and Kan's simplicial loop group functor Décalage and Kan's simplicial loop group functor

2011-12-02

arxiv.org/abs/1112.0474v2

Mathematics

Algebraic Topology

20 pages, added references and table of contents, corrected typos and hopefully improved exposition

Scientific paper

Given a bisimplicial set, there are two ways to extract from it a simplicial set: the diagonal simplicial set and the less well known total simplicial set of Artin and Mazur. There is a natural comparison map between these two simplicial sets, and it is a theorem due to Cegarra and Remedios and independently Joyal and Tierney, that this comparison map is a weak equivalence for any bisimplicial set. In this paper we will give a new, elementary proof of this result. As an application, we will revisit Kan's simplicial loop group functor G. We will give a simple formula for this functor, which is based on a factorization, due to Duskin, of Eilenberg and Mac Lane's classifying complex functor Wbar. We will give a new, short, proof of Kan's result that the unit map for the adjunction (G,Wbar) is a weak equivalence for reduced simplicial sets.

Affiliated with

Also associated with

No associations

Rating

Décalage and Kan's simplicial loop group functor 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 Décalage and Kan's simplicial loop group functor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Décalage and Kan's simplicial loop group functor will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-140415