Cartesian Cubical Model Categories (Lecture Notes in Mathematics, 2385) - Softcover

Awodey, Steve

 
9783032087294: Cartesian Cubical Model Categories (Lecture Notes in Mathematics, 2385)
Softcover
ISBN 10: 3032087295 ISBN 13: 9783032087294
Verlag: Springer, 2026

Inhaltsangabe

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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Über die Autorin bzw. den Autor

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.

Von der hinteren Coverseite

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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Verlag
Springer
Erscheinungsdatum
2026
Sprache
Englisch
ISBN 10 
3032087295
ISBN 13 
9783032087294
Einband
Taschenbuch
Anzahl der Seiten
151
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