Model categories

iv Contents Preface vii Chapter 1. Model categories 1 1.1. The definition of a model category 2 1.2. The homotopy category 7 1.3. Quillen functors and derived functors 13 1.3.1. Quillen functors 13 1.3.2. Derived functors and naturality 16 1.3.3. Quillen equivalences 19 1.4. 2-categories and pseudo-2-functors 22 Chapter 2. Examples 27 2.1. Cofibrantly generated model categories 28 2.1.1. Ordinals, cardinals, and transfinite compositions 28 2.1.2. Relative I-cell complexes and the small object argument 30 2.1.3. Cofibrantly generated model categories 34 2.2. The stable category of modules 36 2.3. Chain complexes of modules over a ring 40 2.4. Topological spaces 48 2.5. Chain complexes of comodules over a Hopf algebra 60 2.5.