Polygraphs: From Rewriting to Higher Categories
portes grátis
Polygraphs: From Rewriting to Higher Categories
Mimram, Samuel; Metayer, Francois; Burroni, Albert; Guiraud, Yves; Malbos, Philippe; Ara, Dimitri
Cambridge University Press
04/2025
666
Mole
9781009498982
Pré-lançamento - envio 15 a 20 dias após a sua edição
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Part I. Fundamentals of Rewriting: 1. Abstract rewriting and one-dimensional polygraphs; 2. Two-dimensional polygraphs; 3. Operations on presentations; 4. String rewriting and 2-polygraphs; 5. Tietze transformations and completion; 6. Linear rewriting; Part II. Coherent Presentations: 7. Coherence by convergence; 8. Categories of finite derivation type; 9. Homological syzygies and confluence; Part III. Diagram Rewriting: 10. Three-dimensional polygraphs; 11. Termination of 3-polygraphs; 12. Coherent presentations of 2-categories; 13. Term rewriting systems; Part IV. Polygraphs: 14. Higher categories; 15. Polygraphs; 16. Properties of the category of ??-polygraphs; 17. A catalogue of ??-polygraphs; 18. Generalized polygraphs; Part V. Homotopy Theory of Polygraphs; 19. Polygraphic resolutions; 20. Towards the folk model structure; 21. The folk model structure; 22. Homology of ??-categories; 23. Resolutions by (??, 1)-polygraphs; Appendix A. A catalogue of 2-polygraphs; Appendix B. Examples of coherent presentations of monoids; Appendix C. A catalogue of 3-polygraphs; Appendix D. A syntactic description of free ??-categories; Appendix E. Complexes and homology; Appendix F. Homology of categories; Appendix G. Locally presentable categories; Appendix H. Model categories; References; Index of notations; Index of terminology.Part I. Fundamentals of Rewriting: 1. Abstract rewriting and one-dimensional polygraphs; 2. Two-dimensional polygraphs; 3. Operations on presentations; 4. String rewriting and 2-polygraphs; 5. Tietze transformations and completion; 6. Linear rewriting; Part II. Coherent Presentations: 7. Coherence by convergence; 8. Categories of finite derivation type; 9. Homological syzygies and confluence; Part III. Diagram Rewriting: 10. Three-dimensional polygraphs; 11. Termination of 3-polygraphs; 12. Coherent presentations of 2-categories; 13. Term rewriting systems; Part IV. Polygraphs: 14. Higher categories; 15. Polygraphs; 16. Properties of the category of ??-polygraphs; 17. A catalogue of ??-polygraphs; 18. Generalized polygraphs; Part V. Homotopy Theory of Polygraphs: 19. Polygraphic resolutions; 20. Towards the folk model structure; 21. The folk model structure; 22. Homology of ??-categories; 23. Resolutions by (??, 1)-polygraphs; Appendix A. A catalogue of 2-polygraphs; Appendix B. Examples of coherent presentations of monoids; Appendix C. A catalogue of 3-polygraphs; Appendix D. A syntactic description of free ??-categories; Appendix E. Complexes and homology; Appendix F. Homology of categories; Appendix G. Locally presentable categories; Appendix H. Model categories; References; Index of notations; Index of terminology.
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Part I. Fundamentals of Rewriting: 1. Abstract rewriting and one-dimensional polygraphs; 2. Two-dimensional polygraphs; 3. Operations on presentations; 4. String rewriting and 2-polygraphs; 5. Tietze transformations and completion; 6. Linear rewriting; Part II. Coherent Presentations: 7. Coherence by convergence; 8. Categories of finite derivation type; 9. Homological syzygies and confluence; Part III. Diagram Rewriting: 10. Three-dimensional polygraphs; 11. Termination of 3-polygraphs; 12. Coherent presentations of 2-categories; 13. Term rewriting systems; Part IV. Polygraphs: 14. Higher categories; 15. Polygraphs; 16. Properties of the category of ??-polygraphs; 17. A catalogue of ??-polygraphs; 18. Generalized polygraphs; Part V. Homotopy Theory of Polygraphs; 19. Polygraphic resolutions; 20. Towards the folk model structure; 21. The folk model structure; 22. Homology of ??-categories; 23. Resolutions by (??, 1)-polygraphs; Appendix A. A catalogue of 2-polygraphs; Appendix B. Examples of coherent presentations of monoids; Appendix C. A catalogue of 3-polygraphs; Appendix D. A syntactic description of free ??-categories; Appendix E. Complexes and homology; Appendix F. Homology of categories; Appendix G. Locally presentable categories; Appendix H. Model categories; References; Index of notations; Index of terminology.Part I. Fundamentals of Rewriting: 1. Abstract rewriting and one-dimensional polygraphs; 2. Two-dimensional polygraphs; 3. Operations on presentations; 4. String rewriting and 2-polygraphs; 5. Tietze transformations and completion; 6. Linear rewriting; Part II. Coherent Presentations: 7. Coherence by convergence; 8. Categories of finite derivation type; 9. Homological syzygies and confluence; Part III. Diagram Rewriting: 10. Three-dimensional polygraphs; 11. Termination of 3-polygraphs; 12. Coherent presentations of 2-categories; 13. Term rewriting systems; Part IV. Polygraphs: 14. Higher categories; 15. Polygraphs; 16. Properties of the category of ??-polygraphs; 17. A catalogue of ??-polygraphs; 18. Generalized polygraphs; Part V. Homotopy Theory of Polygraphs: 19. Polygraphic resolutions; 20. Towards the folk model structure; 21. The folk model structure; 22. Homology of ??-categories; 23. Resolutions by (??, 1)-polygraphs; Appendix A. A catalogue of 2-polygraphs; Appendix B. Examples of coherent presentations of monoids; Appendix C. A catalogue of 3-polygraphs; Appendix D. A syntactic description of free ??-categories; Appendix E. Complexes and homology; Appendix F. Homology of categories; Appendix G. Locally presentable categories; Appendix H. Model categories; References; Index of notations; Index of terminology.
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