The Univalence Principle

Benedikt Ahrens, Paige Randall North, Michael Shulman, Dimitris Tsementzis (Autoren)

Buch | Softcover

176 Seiten

2025
American Mathematical Society (Verlag)
978-1-4704-7269-6 (ISBN)

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Publishing new research across pure and applied mathematics, this series compiles extensive, interrelated papers into grouped collections presented in book form. Every contribution is stringently peer-reviewed and curated by an expert editorial committee, ensuring scholarly precision and depth.

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.

Benedikt Ahrens, Delft University of Technology, The Netherlands Paige Randall North, Utrecht University, The Netherlands Michael Shulman, University of San Diego, California Dimitris Tsementzis, Princeton University, New Jersey, and Rutgers University, New Brunswick, New Jersey.

1. Introduction
2. Introduction to two-level homotopy type theory and univalent foundations
1. Theory of Diagram Structures
3. Categories: An extended example
4. Diagram signatures in Two-Level Type Theory
5. Indiscernibility and univalence for diagram structures
6. The univalence principle for diagram structures
2. Examples of Diagram Structures
7. Structured sets
8. Structured 1-categories
9. Higher categories
10. Strict categorical structures
11. Graphs and Petri nets
12. Enhanced categories and higher categories
13. Unnatural transformations and nonfunctorial operations
3. Theory of Functorial Structures
14. Functorial signatures
15. Levelwise equivalences of structures
16. Indiscernibility and univalence
17. Equivalence of structures and the univalence principle
18. Examples of functorial structures
19. Conclusion

Erscheinungsdatum	06.03.2025
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-4704-7269-4 / 1470472694
ISBN-13	978-1-4704-7269-6 / 9781470472696
Zustand	Neuware