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In the mathematical field of category theory, the product of two categories ''C'' and ''D'', denoted and called a product category, is a straightforward extension of the concept of the Cartesian product of two sets. ==Definition== The product category has: *as objects: *:pairs of objects , where ''A'' is an object of ''C'' and ''B'' of ''D''; *as arrows from to : *:pairs of arrows , where is an arrow of ''C'' and is an arrow of ''D''; *as composition, component-wise composition from the contributing categories: *:; *as identities, pairs of identities from the contributing categories: *:1(''A'', ''B'') = (1''A'', 1''B''). 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「product category」の詳細全文を読む スポンサード リンク
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