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Cartesian Cubical Model Categories

By Steve Awodey

Cartesian Cubical Model Categories

By Steve Awodey

0 - Default Title
Description
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.
Product details
Binding:
Paperback
Number of Pages:
152
Release Date:
2026-01-03
Publication Date:
2026-01-03
Publisher:
Springer
Languages:
Original: English
ISBN10:
3032087295
ISBN13:
9783032087294
GPSR Manufacturer Reference:
[email protected]
Weight:
242 g
Height:
155 cm
Width:
235 cm
Thickness:
9 cm
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