Model Categories and Simplicial Methods

Details Model Categories and Simplicial Methods Model Categories and Simplicial Methods

2006-09-19

arxiv.org/abs/math/0609537v2

Mathematics

Algebraic Topology

(Chicago 2004) To appear in the proceedings of the summer school "Interactions between homotopy theory and algebra"

Scientific paper

There are many ways to present model categories, each with a different point of view. Here we'd like to treat model categories as a way to build and control resolutions. This an historical approach, as in his original and spectacular applications of model categories, Quillen used this technology as a way to construct resolutions in non-abelian settings; for example, in his work on the homology of commutative algebras, it was important to be very flexible with the notion of a free resolution of a commutative algebra. Similar issues arose in the paper on rational homotopy theory. (This paper is the first place where the now-traditional axioms of a model category are enunciated.) We're going to emphasize the analog of projective resolutions, simply because these are the sort of resolutions most people see first. Of course, the theory is completely flexible and can work with injective resolutions as well.

Affiliated with

Also associated with

No associations

Rating

Model Categories and Simplicial Methods 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 Model Categories and Simplicial Methods, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Model Categories and Simplicial Methods will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-351386