Homotopy Theory of Higher Categories: From Segal Categories to N-Categories and Beyond

ISBN-13: 9780521516952 / Angielski / Twarda / 2011 / 654 str.

Carlos Simpson

Opis

Develops a full set of homotopical algebra techniques dedicated to the study of higher categories.

Spis treści

Prologue; Acknowledgements; Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. The need for weak composition; 5. Simplicial approaches; 6. Operadic approaches; 7. Weak enrichment over a Cartesian model category: an introduction; Part II. Categorical Preliminaries: 8. Some category theory; 9. Model categories; 10. Cartesian model categories; 11. Direct left Bousfield localization; Part III. Generators and Relations: 12. Precategories; 13. Algebraic theories in model categories; 14. Weak equivalences; 15. Cofibrations; 16. Calculus of generators and relations; 17. Generators and relations for Segal categories; Part IV. The Model Structure: 18. Sequentially free precategories; 19. Products; 20. Intervals; 21. The model category of M-enriched precategories; 22. Iterated higher categories; Part V. Higher Category Theory: 23. Higher categorical techniques; 24. Limits of weak enriched categories; 25. Stabilization; Epilogue; References; Index.