2006/09/19 by Paul G. Goerss, Goerss, Paul G., Kristen Schemmerhorn +1 · 1 citation
Mathematics · #18G55 #55U35 #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0609537
openalex publication_date 2006/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.