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Cartesian cubical model categories Steve Awodey

By: Contributor(s): Material type: TextTextLanguage: English Series: Lecture notes in mathematics ; 2385Publisher: Cham Springer [2026]Copyright date: © 2026Description: xii, 137 Seiten Diagramme 23,5 cmContent type:
  • Text
Media type:
  • ohne Hilfsmittel zu benutzen
Carrier type:
  • Band
ISBN:
  • 9783032087294
Subject(s): Additional physical formats: No title; No title; Erscheint auch als: Cartesian Cubical Model Categories
Contents:
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.
Summary: 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.
List(s) this item appears in: New Books 2026/2 January-February
Holdings
Item type Current library Collection Shelving location Call number Status Date due Barcode
Book Book Gebäude E2 3 (UdS Campusbibliothek für Informatik und Mathematik) Campusbibliothek für Informatik und Mathematik (E2 3) Series (GF) LNM 2385 (Browse shelf(Opens below)) Available 2202000647119

Literaturverzeichnis: Seite 131-134

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.

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.

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