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The Univalence Principle
 
Benedikt Ahrens Delft University of Technology, Delft, The Netherlands
Paige Randall North Utrecht University, Utrecht, The Netherlands
Michael Shulman University of San Diego, San Diego, California
Dimitris Tsementzis Princeton University, Princeton, New Jersey and Rutgers University, New Brunswick, New Jersey
Softcover ISBN:  978-1-4704-7269-6
Product Code:  MEMO/305/1541
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Not yet published - Preorder Now!
Expected availability date: February 20, 2025
eBook ISBN:  978-1-4704-8043-1
Product Code:  MEMO/305/1541.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7269-6
eBook: ISBN:  978-1-4704-8043-1
Product Code:  MEMO/305/1541.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Not yet published - Preorder Now!
Expected availability date: February 20, 2025
Click above image for expanded view
The Univalence Principle
Benedikt Ahrens Delft University of Technology, Delft, The Netherlands
Paige Randall North Utrecht University, Utrecht, The Netherlands
Michael Shulman University of San Diego, San Diego, California
Dimitris Tsementzis Princeton University, Princeton, New Jersey and Rutgers University, New Brunswick, New Jersey
Softcover ISBN:  978-1-4704-7269-6
Product Code:  MEMO/305/1541
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Not yet published - Preorder Now!
Expected availability date: February 20, 2025
eBook ISBN:  978-1-4704-8043-1
Product Code:  MEMO/305/1541.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7269-6
eBook ISBN:  978-1-4704-8043-1
Product Code:  MEMO/305/1541.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Not yet published - Preorder Now!
Expected availability date: February 20, 2025
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 3052025; 176 pp
    MSC: Primary 18; 03; Secondary 55

    View the abstract.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 3052025; 176 pp
MSC: Primary 18; 03; Secondary 55

View the abstract.

  • Chapters
  • 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.