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Product category : ウィキペディア英語版
Product category

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)
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