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024 7 $a10.1007/978-3-032-08730-0
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035   $a(Au-PeEL)EBL32471618
035   $a(DE-He213)978-3-032-08730-0
035   $a(EXLCZ)9944773726000041
100   $a20260103d2026      u|         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aCartesian Cubical Model Categories /$fby Steve Awodey
205   $a1st ed. 2026.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2026.
215   $a1 online resource (220 pages)
225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2385
311 08$a3-032-08729-5 
327   $aChapter 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.
330   $aThis book introduces the category of Cartesian cubical sets and endows it with a Quillen model structure using ideas coming from Homotopy type theory. In particular, recent constructions of cubical systems of univalent type theory are used to determine abstract homotopical semantics of type theory. The celebrated univalence axiom of Voevodsky plays a key role in establishing the basic laws of a model structure, showing that the homotopical interpretation of constructive type theory is not merely possible, but in a certain, precise sense also necessary for the validity of univalence. Fully rigorous proofs are given in diagrammatic style, using the language and methods of categorical logic and topos theory. The intended readers are researchers and graduate students in homotopy theory, type theory, and category theory.
410  0$aLecture Notes in Mathematics,$x1617-9692 ;$v2385
606   $aAlgebraic topology
606   $aLogic, Symbolic and mathematical
606   $aAlgebra, Homological
606   $aAlgebraic Topology
606   $aMathematical Logic and Foundations
606   $aCategory Theory, Homological Algebra
615  0$aAlgebraic topology.
615  0$aLogic, Symbolic and mathematical.
615  0$aAlgebra, Homological.
615 14$aAlgebraic Topology.
615 24$aMathematical Logic and Foundations.
615 24$aCategory Theory, Homological Algebra.
676   $a514.2
700   $aAwodey$b Steve$01276661
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996696982303316
996   $aCartesian Cubical Model Categories$94519851
997   $aUNISA