Cartesian Cubical Model Categories

Erscheinungsjahr 2026
ISBN: 978-3-032-08729-4
Verlag: Springer

Buch, Englisch, Band 2385, 140 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 242 g

Reihe: Lecture Notes in Mathematics

This book introduces the category of Cartesian cubical sets and endows it with a Quillen model structure using ideas coming from Homotopy type theory. In particular, recent constructions of cubical systems of univalent type theory are used to determine abstract homotopical semantics of type theory. The celebrated univalence axiom of Voevodsky plays a key role in establishing the basic laws of a model structure, showing that the homotopical interpretation of constructive type theory is not merely possible, but in a certain, precise sense also necessary for the validity of univalence. Fully rigorous proofs are given in diagrammatic style, using the language and methods of categorical logic and topos theory. The intended readers are researchers and graduate students in homotopy theory, type theory, and category theory.

Zielgruppe

Research

Autoren/Hrsg.

Awodey, Steve

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

Chapter 1. Introduction.- Chapter 2. Cartesian cubical sets.- Chapter 3. The cofibration weak factorization system.- Chapter 4. The fibration weak factorization system.- Chapter 5. The weak equivalences.- Chapter 6. The Frobenius condition.- Chapter 7. A universal fibration.- Chapter 8. The equivalence extension property.- Chapter 9. The fibration extension property.

Über Autor(innen)

Steve Awodey holds the Dean’s Chair in Logic at Carnegie Mellon University, where he is Professor of Philosophy and Mathematics. A founder of Homotopy Type Theory, he co-organized a special research year on Univalent Foundations at the Institute for Advanced Study (Princeton). His numerous publications include the textbook and the collaborative volume . He serves on several journal editorial boards and is coordinating editor of the . He has held visiting appointments at the Poincaré Institute (Paris), Newton Institute (Cambridge), Hausdorff Institute (Bonn), and the Centre for Advanced Studies (Oslo), and is currently a Royal Society Wolfson Visiting Fellow at Cambridge University.