Quillen D.G. Homotopical Algebra

Springer-Verlag, 1967. — 164 p. — (Lecture Notes in Mathematics).A collection of informal reports and seminars
Edited by A. Dold, Heidelberg and B. Eckmann, ZurichDaniel G. Quillen. Massachusetts Institute of Technology
Cambridge, Mass.Homotopical Algebra or nonlinear homological algebra is the generalization of homological algebra to arbitrary categories which results by considering a simplicial object as being a generalization of a chain complex.Axiomatic homotopy theory
The axioms
The loop and suspension functors
Fibration and cofibration sequences
Equivalence of homotopy theories
Closed model categoriesExamples of simplicial homotopy theories
Simplicial categories
Closed simplicial model categories
Topological spaces, simplicial sets, and simplicial groups
sA as a model category
Homology and cohomology
Modules over simplicial rings