Pullback (category theory)
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain. The pullback is often written P = X ×Z Y The dual concept of the pullback is the pushout.
Abelian categoryAdjoint functorsAllegory (mathematics)Arithmetic and geometric FrobeniusAssociated bundleBase change theoremsBeauville–Laszlo theoremBrown's representability theoremBundle (mathematics)Bundle metricCartesianCartesian diagramCartesian productCartesian square (category theory)Categorical pullbackCategory of ringsCoherent sheaf cohomologyCoherent spaceComplete categoryDescent (mathematics)Diagonal morphism (algebraic geometry)Diagram (category theory)Direct image functorDirect product of groupsDuality (mathematics)EmbeddingEqualiser (mathematics)Essential extensionExact categoryExact completionExt functorExtensive categoryFiber (mathematics)Fiber productFiber product of schemesFibered productFibrationFibre productFibred categoryFibred product
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Pullback (category theory)
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain. The pullback is often written P = X ×Z Y The dual concept of the pullback is the pushout.
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En mathématiques, le produit f ...... parfois utilisée en français.
@fr
In category theory, a branch o ...... f the pullback is the pushout.
@en
O produto fibrado (ou pullback) é uma construção de teoria das categorias.
@pt
Расслоённое произведение (посл ...... понятие — кодекартов квадрат.
@ru
圏論という数学の分野において，引き戻し（ひきもどし，英: p ...... である． 引き戻しの双対概念は (pushout) である．
@ja
在范畴论中，一个数学分支，拉回（也称为纤维积或笛卡尔方块）是由具有公共上域的两个态射f : X → Z与g : Y → Z组成的的极限。拉回经常写作
@zh
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En mathématiques, le produit f ...... alité avec la somme amalgamée.
@fr
In category theory, a branch o ...... f the pullback is the pushout.
@en
O produto fibrado (ou pullback) é uma construção de teoria das categorias.
@pt
Расслоённое произведение (посл ...... понятие — кодекартов квадрат.
@ru
圏論という数学の分野において，引き戻し（ひきもどし，英: p ...... である． 引き戻しの双対概念は (pushout) である．
@ja
在范畴论中，一个数学分支，拉回（也称为纤维积或笛卡尔方块）是由具有公共上域的两个态射f : X → Z与g : Y → Z组成的的极限。拉回经常写作
@zh
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Faserprodukt
@de
Produit fibré
@fr
Produto fibrado
@pt
Pullback (category theory)
@en
Расслоённое произведение
@ru
Розшарований добуток
@uk
引き戻し (圏論)
@ja
拉回 (范畴论)
@zh
당김 (범주론)
@ko