Cartesian Cubical Model Categories

Häftad, Engelska, 2026

Del i serien Lecture Notes in Mathematics

694 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2026-01-03
Mått:155 x 235 x 9 mm
Vikt:242 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:140
Förlag:Springer Nature Switzerland AG
ISBN:9783032087294

Utforska kategorier

Matematikens grunder inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik

Mer om författaren

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 Category Theory and the collaborative volume Homotopy Type Theory: Univalent Foundations of Mathematics. He serves on several journal editorial boards and is coordinating editor of the Journal of Symbolic Logic. 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.

Innehållsförteckning

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.