x Contents Chapter 10. Model Categories 261 §10.1. Model Categories 262 §10.2. Left and Right Homotopy 266 §10.3. The Homotopy Category of a Model Category 268 §10.4. Derived Functors and Quillen Equivalence 268 §10.5. Homotopy Limits and Colimits 270 Part 3. Four Topological Inputs Chapter 11. The Concept of Dimension in Homotopy Theory 275 §11.1. Induction Principles for CW Complexes 276 §11.2. n-Equivalences and Connectivity of Spaces 277 §11.3. Reformulations of n-Equivalences 280 §11.4. The J. H. C. Whitehead Theorem 286 §11.5. Additional Problems 286 Chapter 12. Subdivision of Disks 289 §12.1. The Seifert-Van Kampen Theorem 289 §12.2. Simplices and Subdivision 295 §12.3. The Connectivity of Xn X 298 §12.4. Cellular Approximation of Maps 299 §12.5. Homotopy Colimits and n-Equivalences 300 §12.6. Additional Problems and Projects 303 Chapter 13. The Local Nature of Fibrations 305 §13.1. Maps Homotopy Equivalent to Fibrations 306 §13.2. Local Fibrations Are Fibrations 308 §13.3. Gluing Weak Fibrations 310 §13.4. The First Cube Theorem 313 Chapter 14. Pullbacks of Cofibrations 317 §14.1. Pullbacks of Cofibrations 317 §14.2. Pullbacks of Well-Pointed Spaces 319 §14.3. The Second Cube Theorem 320 Chapter 15. Related Topics 323 §15.1. Locally Trivial Bundles 323 §15.2. Covering Spaces 326 §15.3. Bundles Built from Group Actions 330
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