---

＜電子ブック＞
Effective Kan Fibrations in Simplicial Sets / by Benno van den Berg, Eric Faber
(Lecture Notes in Mathematics. ISSN:16179692 ; 2321)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	X, 230 p. 1 illus : online resource
著者標目	*van den Berg, Benno author Faber, Eric author SpringerLink (Online service)
件　名	LCSH:Algebra, Homological LCSH:Mathematical logic FREE:Category Theory, Homological Algebra FREE:Mathematical Logic and Foundations
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-18900-5

 類似資料