Information om | Engelska ordet FIBRATIONS

Exempel på hur man kan använda FIBRATIONS i en mening

• The meanings of different arrows are not entirely standardized: the arrows used for monomorphisms, epimorphisms, and isomorphisms are also used for injections, surjections, and bijections, as well as the cofibrations, fibrations, and weak equivalences in a model category.
• Hurewicz is best remembered for three remarkable contributions to mathematics: his discovery of the higher homotopy groups in 1935–36, his discovery of the long exact homotopy sequence for fibrations in 1941, and the Hurewicz theorem connecting homotopy and homology groups.
• Easy examples of this are elliptic fibrations, smooth morphisms, and morphisms to stratified varieties which satisfy miracle flatness on each of the strata.
• In order to define a model structure on the category of simplicial sets, one has to define fibrations, cofibrations and weak equivalences.
• The normalized symbols of Seifert fibrations with positive orbifold Euler characteristic are given in the list below.
• Quillen has proposed the notion of model category as a formal framework for doing homotopy theory in more general categories; a model category is endowed with three distinguished classes of morphisms called fibrations, cofibrations and weak equivalences satisfying certain lifting and factorization axioms.
• A model category is a category C with three distinguished types of morphisms called fibrations, cofibrations and weak equivalences, satisfying several axioms.
• The most studied Milnor maps are actually fibrations, and the phrase Milnor fibration is more commonly encountered in the mathematical literature.
• The above definition can be succinctly phrased by the following equivalent definition: a model category is a category C and three classes of (so-called) weak equivalences W, fibrations F and cofibrations C so that.
• The theory of fibered spaces, of which vector bundles, principal bundles, topological fibrations and fibered manifolds are a special case, is attributed to Seifert, Hopf, Feldbau, Whitney, Steenrod, Ehresmann, Serre, and others.
• This notion leads to a succinct definition of model categories: a model category is a pair consisting of a category C and classes of (so-called) weak equivalences W, fibrations F and cofibrations C so that.
• Kan complexes are also the fibrant (and cofibrant) objects of model categories of simplicial sets for which the fibrations are Kan fibrations.
• Liftings are used to produce disintegrations of measures, for instance conditional probability distributions given continuous random variables, and fibrations of Lebesgue measure on the level sets of a function.
• The example that started the subject is the category of topological spaces with Serre fibrations as fibrations and weak homotopy equivalences as weak equivalences (the cofibrations for this model structure can be described as the retracts of relative cell complexes X ⊆ Y).
• Dually, there is a notion of right Bousfield localization, whose definition is obtained by replacing cofibrations by fibrations (and reversing directions of all arrows).
• The Strominger–Yau–Zaslow conjecture: From torus fibrations to degenerations, AMS Symposium Algebraic Geometry, Seattle 2005, Preprint 2008,.

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