Model category theory, first developed in the late 1960’s by Quillen, has become very popular among algebraic topologists and algebraic geometers in the past decade. A model category is a category endowed with three distinguished classes of morphisms –fibrations, cofibrations and weak equivalences– satisfying axioms that are properties of the topological category and its usual fibrations, cofibrations and weak equivalences. In any model category there is a notion of homotopy of morphisms, based on the definition of homotopy of continuous maps.
The purpose of this course is to provide an introduction to model category theory, complete with numerous examples of model categories and their applications in algebra and topology.
Starting date: October 23, 2003
Schedule: Thursdays, from 8:30 to 11:00
Room: MA/30 (EXCEPT 11.12.03 and 08.01.04, when we will be in CM100.)
The goals of homotopical algebra
The homotopy theory of topological spaces
Basic category theory
Elementary model category theory
Definition, examples and properties of model categories
The homotopy relation in a model category
The homotopy category of a model category
Derived functors, Quillen pairs and Quillen equivalences