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001451969 019__ $$a1354630830$$a1355219829$$a1355372669
001451969 020__ $$a9783031189005$$q(electronic bk.)
001451969 020__ $$a3031189000$$q(electronic bk.)
001451969 020__ $$z9783031188992
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001451969 0247_ $$a10.1007/978-3-031-18900-5$$2doi
001451969 035__ $$aSP(OCoLC)1356272248
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001451969 050_4 $$aQA612.7
001451969 08204 $$a514/.24$$223/eng/20221227
001451969 1001_ $$aBerg, Benno van den,$$eauthor.
001451969 24510 $$aEffective Kan fibrations in simplicial sets /$$cBenno van den Berg, Eric Faber.
001451969 264_1 $$aCham :$$bSpringer,$$c[2022]
001451969 264_4 $$c©2022
001451969 300__ $$a1 online resource (x, 230 pages) :$$billustrations.
001451969 336__ $$atext$$btxt$$2rdacontent
001451969 337__ $$acomputer$$bc$$2rdamedia
001451969 338__ $$aonline resource$$bcr$$2rdacarrier
001451969 4901_ $$aLecture notes in mathematics ;$$vvolume 2321
001451969 504__ $$aIncludes bibliographical references and index.
001451969 5058_ $$a4 An Algebraic Weak Factorisation System from a Moore Structure -- 4.1 Defining the Algebraic Weak Factorisation System -- 4.1.1 Functorial Factorisation -- 4.1.2 The Comonad -- 4.1.3 The Monad -- 4.1.4 The Distributive Law -- 4.2 Hyperdeformation Retracts -- 4.2.1 Hyperdeformation Retracts are Coalgebras -- 4.2.2 Hyperdeformation Retracts are Bifibred -- 4.3 Naive Fibrations -- 5 The Frobenius Construction -- 5.1 Naive Left Fibrations -- 5.2 The Frobenius Construction -- 6 Mould Squares and Effective Fibrations -- 6.1 A New Notion of Fibred Structure -- 6.2 Effective Fibrations
001451969 5058_ $$a6.2.1 Effective Trivial Fibrations -- 6.2.2 Right and Left Fibrations -- 7 -Types -- Part II Simplicial Sets -- 8 Effective Trivial Kan Fibrations in Simplicial Sets -- 8.1 Effective Cofibrations -- 8.2 Effective Trivial Kan Fibrations -- 8.3 Local Character and Classical Correctness -- 9 Simplicial Sets as a Symmetric Moore Category -- 9.1 Polynomial Yoga -- 9.2 A Simplicial Poset of Traversals -- 9.3 Simplicial Moore Paths -- 9.4 Geometric Realization of a Traversal -- 10 Hyperdeformation Retracts in Simplicial Sets -- 10.1 Hyperdeformation Retracts Are Effective Cofibrations
001451969 5058_ $$a10.2 Hyperdeformation Retracts as Internal Presheaves -- 10.3 A Small Double Category of Hyperdeformation Retracts -- 10.4 Naive Kan Fibrations in Simplicial Sets -- 11 Mould Squares in Simplicial Sets -- 11.1 Small Mould Squares -- 11.2 Effective Kan Fibrations in Terms of ``Filling'' -- 12 Horn Squares -- 12.1 Effective Kan Fibrations in Terms of Horn Squares -- 12.2 Local Character and Classical Correctness -- 13 Conclusion -- 13.1 Properties of Effective Kan Fibrations -- 13.2 Directions for Future Research -- A Axioms -- A.1 Moore Structure -- A.2 Dominance -- B Cubical Sets
001451969 5058_ $$aC Degenerate Horn Fillers Are Unique -- D Uniform Kan Fibrations -- References -- Index
001451969 506__ $$aAccess limited to authorized users.
001451969 520__ $$aThis 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.
001451969 588__ $$aDescription based on print version record.
001451969 650_0 $$aHomotopy theory.
001451969 655_0 $$aElectronic books.
001451969 7001_ $$aFaber, Eric,$$eauthor.
001451969 77608 $$iPrint version:$$aBerg, Benno van den.$$tEffective Kan fibrations in simplicial sets.$$dCham : Springer, 2022$$z9783031188992$$w(OCoLC)1346951082
001451969 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2321.
001451969 852__ $$bebk
001451969 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-18900-5$$zOnline Access$$91397441.1
001451969 909CO $$ooai:library.usi.edu:1451969$$pGLOBAL_SET
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001451969 980__ $$aEBOOK
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