Titlebook: Effective Kan Fibrations in Simplicial Sets; Benno van den Berg,Eric Faber Book 2022 The Editor(s) (if applicable) and The Author(s), unde

Scintillations

An Algebraic Weak Factorisation System from a Dominance factorisation system will be shown to be the class of . defined by the dominance, while the right class (algebras) is called the class of .. Proposition . can also be found in Bourke and Garner [.]. The rest of the chapter studies the (double) category of effective cofibrations a bit more closely a

使習(xí)慣于

Mortar

machination

Mould Squares and Effective Fibrationsy ingredient in this definition is the notion of a specific morphism between hyperdeformation retracts, called a .. After defining mould squares, effective fibrations are defined as arrows equipped with a right-lifting property with respect to a triple category of hyperdeformation retracts and mould

精致

ONYM

Effective Trivial Kan Fibrations in Simplicial Setsn which the effective cofibrations are the left maps. The right maps in this AWFS will be called the effective trivial Kan fibrations. We show that this class of effective trivial Kan fibrations is cofibrantly generated by a small double category, local and coincides with the usual class of trivial

Temporal-Lobe

Hyperdeformation Retracts in Simplicial Setsus that we will then obtain an AWFS of hyperdeformation retracts and naive Kan fibrations. We show that in the category of simplicial sets the naive Kan fibration are cofibrantly generated by a small double category and are a local notion of fibred structure.

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0075-8434 hese 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.978-3-031-18899-2978-3-031-18900-5Series ISSN 0075-8434 Series E-ISSN 1617-9692

WAIL

Highbrow