Model Categories and Simplicial Methods
By Paul G. Goerss, K. Schemmerhorn. 2006
84 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6f596a5b0bb9362c31e71d9fb72c88b6fef3e6db
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Citations in the corpus
- Rational homotopy theory: a brief introduction (2006, methodology): “7 in [20], to show that this adjoint pair satisfies the hypotheses of Theorem 3.”
- A Darboux theorem for derived schemes with shifted symplectic structure (2013, unknown): “A standard argument (see for instance Goerss and Schemmerhorn [12, Th. 3.6]) shows that in characteristic 0 this choice of weak equivalences and fibrations define a model structure on cdgas.”
- Homotopy completion and topological Quillen homology of structured ring spectra (2011, methodology): “A useful introduction to Quillen homology is given in GoerssSchemmerhorn [28]; see also Goerss [24] and H.”