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Effective Kan Fibrations in Simplicial Sets by Benno van den Berg at Abbey's Bookshop,
Effective Kan Fibrations in Simplicial Sets
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Benno van den Berg Eric Faber

Effective Kan Fibrations in Simplicial Sets

Benno van den Berg,  Eric Faber

$133.95   $107.34

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English
Springer International Publishing AG
10 December 2022
Mathematical foundations; Algebraic topology
Series: Lecture Notes in Mathematics
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.
By:   ,
Imprint:   Springer International Publishing AG
Country of Publication:   Switzerland
Edition:   1st ed. 2022
Volume:   2321
Dimensions:   Height: 235mm,  Width: 155mm, 
Weight:   379g
ISBN:   9783031188992
ISBN 10:   3031188993
Series:   Lecture Notes in Mathematics
Pages:   230
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active

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