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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 and with a common codomain; it is the limit of the cospan . The pullback is often written :. The categorical dual of a pullback is a called a ''pushout''. Remarks opposite to the above apply: the pushout is a coproduct with additional structure. ==Universal property== Explicitly, the pullback of the morphisms and consists of an object and two morphisms and for which the diagram : commutes. Moreover, the pullback must be universal with respect to this diagram. That is, for any other such triple for which the following diagram commutes, there must exist a unique (called a mediating morphism) such that : : As with all universal constructions, the pullback, if it exists, is unique up to isomorphism. In fact, given two pullbacks and of the same cospan, there is a unique isomorphism between and respecting the pullback structure. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pullback (category theory)」の詳細全文を読む スポンサード リンク
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