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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: it is the colimit of the span . The pushout is the categorical dual of the pullback. ==Universal property== Explicitly, the pushout of the morphisms ''f'' and ''g'' consists of an object ''P'' and two morphisms ''i''1 : ''X'' → ''P'' and ''i''2 : ''Y'' → ''P'' such that the diagram : commutes and such that (''P'', ''i''1, ''i''2) is universal with respect to this diagram. That is, for any other such set (''Q'', ''j''1, ''j''2) for which the following diagram commutes, there must exist a unique ''u'' : ''P'' → ''Q'' also making the diagram commute: : As with all universal constructions, the pushout, if it exists, is unique up to a unique isomorphism. 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「Pushout (category theory)」の詳細全文を読む スポンサード リンク
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