Pushout (category theory)
In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain. The pushout consists of an object P along with two morphisms X → P and Y → P that complete a commutative square with the two given morphisms f and g. In fact, the defining universal property of the pushout (given below) essentially says that the pushout is the "most general" way to complete this commutative square. Common notations for the pushout are and .
Abelian categoryAdhesive categoryAdjoint functorsAdjunction spaceAmalgamation propertyAmalgamed sumBlakers–Massey theoremCategory of topological spacesCocartesian squareCoequalizerCofiber productCofibered productCofibrationComplete categoryComplex projective spaceDiagonal functorDiagram (category theory)Double pushout graph rewritingExact categoryExt functorFiber coproductFibered coproductFibered sumFree productFundamental groupGraph rewritingHomotopy colimitK-theory of a categoryLifting propertyLimit (category theory)Mapping cylinderOutline of category theoryPostnikov systemPre-abelian categoryProductPulation squarePullback (category theory)PushforwardPushout (mathematics)Pushout map
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Pushout (category theory)
In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain. The pushout consists of an object P along with two morphisms X → P and Y → P that complete a commutative square with the two given morphisms f and g. In fact, the defining universal property of the pushout (given below) essentially says that the pushout is the "most general" way to complete this commutative square. Common notations for the pushout are and .
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Das Pushout (auch Kofaserprodu ...... m Pullback duale Konstruktion.
@de
En mathématiques, la somme ama ...... pushout (« poussé en avant »).
@fr
In category theory, a branch o ...... egorical dual of the pullback.
@en
Кодекартов квадрат (также — ун ...... тся частным случаем копредела.
@ru
Розшарований кодобуток (також ...... ається кодекартовим квадратом.
@uk
在范畴论中,一个数学领域, 推出(也称为纤维餘积、纤维和、共 ...... X 与 g : Z → Y 组成的的餘极限。 推出是拉回的。
@zh
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Das Pushout (auch Kofaserprodu ...... m Pullback duale Konstruktion.
@de
En mathématiques, la somme ama ...... ide du théorème de van Kampen.
@fr
In category theory, a branch o ...... ions for the pushout are and .
@en
Кодекартов квадрат (также — ун ...... тся частным случаем копредела.
@ru
Розшарований кодобуток (також ...... ається кодекартовим квадратом.
@uk
在范畴论中,一个数学领域, 推出(也称为纤维餘积、纤维和、共 ...... X 与 g : Z → Y 组成的的餘极限。 推出是拉回的。
@zh
label
Pushout (category theory)
@en
Pushout
@de
Somme amalgamée
@fr
Кодекартов квадрат
@ru
Розшарований кодобуток
@uk
推出 (范畴论)
@zh
밂 (범주론)
@ko