Del 2385 - Lecture Notes in Mathematics

Cartesian Cubical Model Categories

Nyhet

Häftad, Engelska, 2026

1 299 kr

Kommande

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

Utgivningsdatum2026-01-06
Mått155 x 235 x undefined mm
FormatHäftad
SpråkEngelska
SerieLecture Notes in Mathematics
FörlagSpringer Nature Switzerland AG
ISBN9783032087294

Tillhör följande kategorier

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

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.