Articles liés à Effective Kan Fibrations in Simplicial Sets
Synopsis
This book introduces the notion of an effective Kan fibration, a new mathematical structure which can be used to study simplicial homotopy theory. The main motivation is to make simplicial homotopy theory suitable for homotopy type theory. Effective Kan fibrations are maps of simplicial sets equipped with a structured collection of chosen lifts that satisfy certain non-trivial properties. Here it is revealed that fundamental properties of ordinary Kan fibrations can be extended to explicit constructions on effective Kan fibrations. In particular, a constructive (explicit) proof is given that effective Kan fibrations are stable under push forward, or fibred exponentials. Further, it is shown that effective Kan fibrations are local, or completely determined by their fibres above representables, and the maps which can be equipped with the structure of an effective Kan fibration are precisely the ordinary Kan fibrations. Hence implicitly, both notions still describe the same homotopy theory. These new results solve an open problem in homotopy type theory and provide the first step toward giving a constructive account of Voevodsky’s model of univalent type theory in simplicial sets.
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Effective Kan Fibrations in Simplicial Sets (Lecture Notes in Mathematics)
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Springer (edition 1st ed. 2022), 2022
ISBN 10 : 3031188993
ISBN 13 : 9783031188992
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Paperback. Etat : Very Good. 1st ed. 2022. It's a well-cared-for item that has seen limited use. The item may show minor signs of wear. All the text is legible, with all pages included. It may have slight markings and/or highlighting. N° de réf. du vendeur 3031188993-8-1
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Effective Kan Fibrations in Simplicial Sets
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Springer International Publishing AG, CH, 2022
ISBN 10 : 3031188993
ISBN 13 : 9783031188992
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Paperback. Etat : New. 1st ed. 2022. This book introduces the notion of an effective Kan fibration, a new mathematical structure which can be used to study simplicial homotopy theory. The main motivation is to make simplicial homotopy theory suitable for homotopy type theory. Effective Kan fibrations are maps of simplicial sets equipped with a structured collection of chosen lifts that satisfy certain non-trivial properties. Here it is revealed that fundamental properties of ordinary Kan fibrations can be extended to explicit constructions on effective Kan fibrations. In particular, a constructive (explicit) proof is given that effective Kan fibrations are stable under push forward, or fibred exponentials. Further, it is shown that effective Kan fibrations are local, or completely determined by their fibres above representables, and the maps which can be equipped with the structure of an effective Kan fibration are precisely the ordinary Kan fibrations. Hence implicitly, both notions still describe the same homotopy theory. These new results solve an open problem in homotopy type theory and provide the first step toward giving a constructive account of Voevodsky's model of univalent type theory in simplicial sets. N° de réf. du vendeur LU-9783031188992
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Effective Kan Fibrations in Simplicial Sets (Lecture Notes in Mathematics)
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Effective Kan Fibrations in Simplicial Sets
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Effective Kan Fibrations in Simplicial Sets (Lecture Notes in Mathematics)
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Effective Kan Fibrations in Simplicial Sets (Paperback)
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Springer International Publishing AG, Cham, 2022
ISBN 10 : 3031188993
ISBN 13 : 9783031188992
Neuf
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Paperback. Etat : new. Paperback. This book introduces the notion of an effective Kan fibration, a new mathematical structure which can be used to study simplicial homotopy theory. The main motivation is to make simplicial homotopy theory suitable for homotopy type theory. Effective Kan fibrations are maps of simplicial sets equipped with a structured collection of chosen lifts that satisfy certain non-trivial properties. Here it is revealed that fundamental properties of ordinary Kan fibrations can be extended to explicit constructions on effective Kan fibrations. In particular, a constructive (explicit) proof is given that effective Kan fibrations are stable under push forward, or fibred exponentials. Further, it is shown that effective Kan fibrations are local, or completely determined by their fibres above representables, and the maps which can be equipped with the structure of an effective Kan fibration are precisely the ordinary Kan fibrations. Hence implicitly, both notions still describe the same homotopy theory. These new results solve an open problem in homotopy type theory and provide the first step toward giving a constructive account of Voevodskys model of univalent type theory in simplicial sets. Further, it is shown that effective Kan fibrations are local, or completely determined by their fibres above representables, and the maps which can be equipped with the structure of an effective Kan fibration are precisely the ordinary Kan fibrations. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9783031188992
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Effective Kan Fibrations in Simplicial Sets
Edité par
Springer International Publishing Dez 2022, 2022
ISBN 10 : 3031188993
ISBN 13 : 9783031188992
Neuf
Taschenbuch
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book introduces the notion of an effective Kan fibration, a new mathematical structure which can be used to study simplicial homotopy theory. The main motivation is to make simplicial homotopy theory suitable for homotopy type theory. Effective Kan fibrations are maps of simplicial sets equipped with a structured collection of chosen lifts that satisfy certain non-trivial properties. Here it is revealed that fundamental properties of ordinary Kan fibrations can be extended to explicit constructions on effective Kan fibrations. In particular, a constructive (explicit) proof is given that effective Kan fibrations are stable under push forward, or fibred exponentials. Further, it is shown that effective Kan fibrations are local, or completely determined by their fibres above representables, and the maps which can be equipped with the structure of an effective Kan fibration are precisely the ordinary Kan fibrations. Hence implicitly, both notions still describe the same homotopy theory. These new results solve an open problem in homotopy type theory and provide the first step toward giving a constructive account of Voevodsky's model of univalent type theory in simplicial sets. 244 pp. Englisch. N° de réf. du vendeur 9783031188992
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Effective Kan Fibrations In Simplicial S
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Effective Kan Fibrations in Simplicial Sets: 2321
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Effective Kan Fibrations in Simplicial Sets: 2321
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