viii Contents Part 2. Semi-Formal Homotopy Theory Chapter 3. Categories of Spaces 45 §3.1. Spheres and Disks 45 §3.2. CW Complexes 46 §3.3. Example: Projective Spaces 51 §3.4. Topological Spaces 53 §3.5. The Category of Pairs 58 §3.6. Pointed Spaces 60 §3.7. Relating the Categories of Pointed and Unpointed Spaces 63 §3.8. Suspension and Loop 66 §3.9. Additional Problems and Projects 68 Chapter 4. Homotopy 69 §4.1. Homotopy of Maps 69 §4.2. Constructing Homotopies 74 §4.3. Homotopy Theory 80 §4.4. Groups and Cogroups in the Homotopy Category 84 §4.5. Homotopy Groups 87 §4.6. Homotopy and Duality 89 §4.7. Homotopy in Mapping Categories 91 §4.8. Additional Problems 98 Chapter 5. Cofibrations and Fibrations 99 §5.1. Cofibrations 100 §5.2. Special Properties of Cofibrations of Spaces 104 §5.3. Fibrations 107 §5.4. Factoring through Cofibrations and Fibrations 110 §5.5. More Homotopy Theory in Categories of Maps 115 §5.6. The Fundamental Lifting Property 118 §5.7. Pointed Cofibrations and Fibrations 122 §5.8. Well-Pointed Spaces 124 §5.9. Exact Sequences, Cofibers and Fibers 129 §5.10. Mapping Spaces 133 §5.11. Additional Topics, Problems and Projects 136 Chapter 6. Homotopy Limits and Colimits 143 §6.1. Homotopy Equivalence in Diagram Categories 144
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