Lifting property
http://dbpedia.org/resource/Lifting_property
Die Hochhebungseigenschaft (englisch Lifting property) ist ein Begriff aus der Kategorientheorie. Er bezeichnet eine Eigenschaft zweier Morphismen. Sie spielt eine wichtige Rolle in der Theorie der Modellkategorien. Ein wichtiger Spezialfall der Hochhebungsseigenschaft ist die Homotopie-Hochhebungseigenschaft aus der Topologie.
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In mathematics, in particular in category theory, the lifting property is a property of a pair of morphisms in a category. It is used in homotopy theory within algebraic topology to define properties of morphisms starting from an explicitly given class of morphisms. It appears in a prominent way in the theory of model categories, an axiomatic framework for homotopy theory introduced by Daniel Quillen. It is also used in the definition of a factorization system, and of a weak factorization system, notions related to but less restrictive than the notion of a model category. Several elementary notions may also be expressed using the lifting property starting from a list of (counter)examples.
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Hochhebungseigenschaft
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Lifting property
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53659730
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1016937453
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Die Hochhebungseigenschaft (englisch Lifting property) ist ein Begriff aus der Kategorientheorie. Er bezeichnet eine Eigenschaft zweier Morphismen. Sie spielt eine wichtige Rolle in der Theorie der Modellkategorien. Ein wichtiger Spezialfall der Hochhebungsseigenschaft ist die Homotopie-Hochhebungseigenschaft aus der Topologie.
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In mathematics, in particular in category theory, the lifting property is a property of a pair of morphisms in a category. It is used in homotopy theory within algebraic topology to define properties of morphisms starting from an explicitly given class of morphisms. It appears in a prominent way in the theory of model categories, an axiomatic framework for homotopy theory introduced by Daniel Quillen. It is also used in the definition of a factorization system, and of a weak factorization system, notions related to but less restrictive than the notion of a model category. Several elementary notions may also be expressed using the lifting property starting from a list of (counter)examples.
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13293
