MODEL CATEGORIES
CONTENTS CHAPTER 1 MODEL CATEGORIES 1 1 THE DE?NITION OF A MODEL CATEGORY 1 2 THE HOMOTOPY CATEGORY 1 3 QUILLEN FUNCTORS AND DERIVED FUNCTORS 1 3 1 QUILLEN FUNCTORS 1 3 2 DERIVED FUNCTORS AND NATURALITY 1 3 3 QUILLEN EQUIVALENCES 1 4 2-CATEGORIES AND PSEUDO-2-FUNCTORS CHAPTER 2 EXAMPLES 2 1 CO?BRANTLY GENERATED MODEL CATEGORIES 2 1 1 ORDINALS, CARDINALS, AND TRANS?NITE COMPOSITIONS 2 1 2 RELATIVE I-CELL COMPLEXES AND THE SMALL OBJECT ARGUMENT 2 1 3 CO?BRANTLY GENERATED MODEL CATEGORIES 2 2 THE STABLE CATEGORY OF MODULES 2 3 CHAIN COMPLEXES OF MODULES OVER A RING 2 4 TOPOLOGICAL SPACES 2 5 CHAIN COMPLEXES OF COMODULES OVER A HOPF ALGEBRA 2 5 1 THE CATEGORY OF B-COMODULES 2 5 2 WEAK EQUIVALENCES 2 5 3 THE MODEL STRUCTURE CHAPTER 3 SIMPLICIAL SETS 3 1 SIMPLICIAL SETS 3 2 THE MODEL STRUCTURE ON SIMPLICIAL SETS 3 3 ANODYNE EXTENSIONS 3 4 HOMOTOPY GROUPS 3 5 MINIMAL ?BRATIONS 3 6 FIBRATIONS AND GEOMETRIC REALIZATION CHAPTER 4 MONOIDAL MODEL CATEGORIES 4 1 CLOSED MONOIDAL CATEGORIES AND CLOSED MODULES 4 2 MONOIDAL MODEL CATEGORIES AND MODULES OVER THEM 4 3 THE HOMOTOPY CATEGORY OF A MONOIDAL MODEL CATEGORY CHAPTER 5 FRAMINGS 5 1 DIAGRAM CATEGORIES 5 2 DIAGRAMS OVER REEDY CATEGORIES AND FRAMINGS 5 3 A LEMMA ABOUT BISIMPLICIAL SETS 5 4 FUNCTION COMPLEXES 5 5 ASSOCIATIVITY 5 6 NATURALITY 5 7 FRAMINGS ON POINTED MODEL CATEGORIES CHAPTER 6 POINTED MODEL CATEGORIES 6 1 THE SUSPENSION AND LOOP FUNCTORS 6 2 CO?BER AND ?BER SEQUENCES 6 3 PROPERTIES OF CO?BER AND ?BER SEQUENCES 6 4 NATURALITY OF CO?BER SEQUENCES 6 5 PRE-TRIANGULATED CATEGORIES 6 6 POINTED MONOIDAL MODEL CATEGORIES CHAPTER 7 STABLE MODEL CATEGORIES AND TRIANGULATED CATEGORIES 7 1 TRIANGULATED CATEGORIES 7 2 STABLE HOMOTOPY CATEGORIES 7 3 WEAK GENERATORS 7 4 FINITELY GENERATED MODEL CATEGORIES CHAPTER 8 VISTAS