About: Lifting property

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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.

Attributes	Values
rdfs:label	Hochhebungseigenschaft (de) Lifting property (en)
rdfs:comment	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. (de) 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. (en)
foaf:depiction
dcterms:subject	Category theory
Wikipage page ID	53659730 (xsd:integer)
Wikipage revision ID	1016937453 (xsd:integer)
Link from a Wikipage to another Wikipage	Pullback (category theory) Module (mathematics) Coproduct (category theory) Morphism (category theory) Algebraic topology Injective module Weak factorization system Sierpinski space Connected component (topology) Continuous function Mathematics Normal space Connected space Commutative ring Complete metric space Dense set Embedding Subgroup Hausdorff space Cyclic group Daniel Quillen Isomorphism Kolmogorov space Product (category theory) Projective module Group (mathematics) Surjective Category theory Homotopy lifting property Homotopy theory Torsion (algebra) Trivial topology Discrete space Disjoint union Free group Metric space Order (group theory) Category (mathematics) Category theory Chain complex Set (mathematics) Factorization system Image (mathematics) Finite group Pushout (category theory) Pure subgroup Real line Simplicial set Injective Topological space P-group Subset Uniformly continuous T1 space Preimage Soluble group Filtered colimit Diagram chasing Model categories
Link from a Wikipage to an external page	https://archive.org/details/arxiv-math9803002
sameAs	Lifting property Lifting property Lifting property
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:One_source dbt:Reflist
thumbnail	wiki-commons:Special:FilePath/Model_category_lifting.png?width=300
has abstract	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. (de) 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. (en)
prov:wasDerivedFrom	wikipedia-en:Lifting_property?oldid=1016937453&ns=0
page length (characters) of wiki page	13293 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Lifting_property
is Link from a Wikipage to another Wikipage of	Lift (mathematics) Profinite group Normal space Constructive set theory Hausdorff space Projective module Covering space Right-lifting-property Right lifting property Homotopy lifting property T1 space Stinespring dilation theorem Left lifting property
is Wikipage redirect of	Right-lifting-property Right lifting property Left lifting property
is foaf:primaryTopic of	wikipedia-en:Lifting_property

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