About: Injective object

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In mathematics, especially in the field of category theory, the concept of injective object is a generalization of the concept of injective module. This concept is important in cohomology, in homotopy theory and in the theory of model categories. The dual notion is that of a projective object.

Attributes	Values
rdfs:label	Injektives Objekt (de) Injective object (en) 単射的対象 (ja) 단사 대상 (ko) Инъективный объект (ru) Ін'єктивний об'єкт (uk)
rdfs:comment	Injektives Objekt ist ein Begriff aus dem mathematischen Teilgebiet der Kategorientheorie. (de) In mathematics, especially in the field of category theory, the concept of injective object is a generalization of the concept of injective module. This concept is important in cohomology, in homotopy theory and in the theory of model categories. The dual notion is that of a projective object. (en) 数学，特に圏論において，単射的対象（たんしゃてきたいしょう，英: injective object, あるいは移入的対象，入射的対象）の概念は単射的加群の概念の一般化である．この概念はホモトピー論とモデル圏の理論において重要である．双対概念は射影的対象である． (ja) 범주론에서 단사 대상(單射對象, 영어: injective object)은 이 대상을 공역으로 삼는 사상의 정의역을 임의로 확장할 수 있는 대상이다. 단사 가군의 개념을 일반화한 개념이다. 마찬가지로, 이에 대한 쌍대 개념인 사영 대상(射影對象, 영어: projective object)은 이 대상을 정의역으로 삼는 사상의 공역을 임의로 축소할 수 있는 대상이다. (ko) Ін'єктивний об'єкт — теоретико-категорне узагальнення поняття ін'єктивних модулів. Двоїстим є поняття проєктивного об'єкта. (uk) Инъективный объект — теоретико-категорное обобщение понятия инъективного модуля. Двойственное понятие — проективный объект. (ru)
foaf:depiction
dcterms:subject	Category theory
Wikipage page ID	473779 (xsd:integer)
Wikipage revision ID	1108128086 (xsd:integer)
Link from a Wikipage to another Wikipage	Module (mathematics) Monomorphism Algebraic topology Dedekind–MacNeille completion Derived functor Injective hull Injective metric space Injective module Ringed space Continuous mapping Mathematics Essential monomorphism Class (set theory) Morphism Order-embedding Locally compact Complete lattice Functor category Tight span Divisible group Sheaf of modules Algebraic geometry Partially ordered set Projective object Group homomorphism Surjective Category theory Abelian category Abelian group T0 space Cohomology Hom functor Homotopy theory Tor functor Model category Module homomorphism Splitting lemma Continuous lattice Grothendieck category Group theory Scott topology If and only if Injective resolution Category (mathematics) Category of metric spaces Category theory Sober space Up to Ext functor Exact functor Exact sequence Simplicial set Kan complex Object (category theory) Monotone map
Link from a Wikipage to an external page	http://www.tac.mta.ca/tac/reprints/articles/17/tr17.pdf
sameAs	Injective object Injective object Injective object Injective object Injective object Injective object Injective object Injective object Injective object
dbp:wikiPageUsesTemplate	dbt:Math dbt:No_footnotes dbt:Reflist dbt:Short_description dbt:Var dbt:Mathcal
thumbnail	wiki-commons:Special:FilePath/Diagrammadefinizionemoduloiniettivo.png?width=300
Link from a Wikipa... related subject.	dbpedia-de:Injektiver_Modul
has abstract	Injektives Objekt ist ein Begriff aus dem mathematischen Teilgebiet der Kategorientheorie. (de) In mathematics, especially in the field of category theory, the concept of injective object is a generalization of the concept of injective module. This concept is important in cohomology, in homotopy theory and in the theory of model categories. The dual notion is that of a projective object. (en) 数学，特に圏論において，単射的対象（たんしゃてきたいしょう，英: injective object, あるいは移入的対象，入射的対象）の概念は単射的加群の概念の一般化である．この概念はホモトピー論とモデル圏の理論において重要である．双対概念は射影的対象である． (ja) 범주론에서 단사 대상(單射對象, 영어: injective object)은 이 대상을 공역으로 삼는 사상의 정의역을 임의로 확장할 수 있는 대상이다. 단사 가군의 개념을 일반화한 개념이다. 마찬가지로, 이에 대한 쌍대 개념인 사영 대상(射影對象, 영어: projective object)은 이 대상을 정의역으로 삼는 사상의 공역을 임의로 축소할 수 있는 대상이다. (ko) Ін'єктивний об'єкт — теоретико-категорне узагальнення поняття ін'єктивних модулів. Двоїстим є поняття проєктивного об'єкта. (uk) Инъективный объект — теоретико-категорное обобщение понятия инъективного модуля. Двойственное понятие — проективный объект. (ru)
gold:hypernym	Generalization
prov:wasDerivedFrom	wikipedia-en:Injective_object?oldid=1108128086&ns=0

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