The Univalence Principle (Memoirs of the American Mathematical Society)

Ahrens, Benedikt/ North, Paige Randall/ Shulman, Michael

American Mathematical Society（2025/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 176 p.
• 言語 ENG
• 商品コード 9781470472696

Full Description

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.

Contents

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