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Catalogue Information
Field name	Details
Dewey Class	512.6
Title	Effective Kan Fibrations in Simplicial Sets ([EBook]) / Benno van den Berg, Eric Faber
Author	Berg, Benno van den
Added Personal Name	Faber, Eric
Publication	Cham : Springer International Publishing , 2023
Physical Details	: online resource (x, 230p., ill.)
Series	Lecture Notes in Mathematics ; 2321
ISBN	978-3-031-18900-5
Summary Note	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.(provided by publisher):
Mode of acces to digital resource	Digital reproduction.- Cham : Springer International Publishing, 2023. - Digital book. Cham Springer Nature 2023. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-031-18900-5
Links to Related Works	Subject References: Category Theory . Homological algebra . Mathematical logic . Authors: Berg, Benno van den . Faber, Eric . Series: Lecture Notes in Mathematics . Classification: 512.6 .

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Effective Kan Fibrations in Simplicial Sets

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