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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Auto magma object ： ウィキペディア英語版 Auto magma object In mathematics, a magma in a category, or magma object, can be defined in a category with a cartesian product. This is the 'internal' form of definition of a binary operation in a category. As Mag the magma category has direct products, the concept of an (internal) magma (or ''internal binary operation'') in Mag is defined, say $\backslash top\text{'}\backslash colon\; (X,\backslash top)\backslash times(X,\backslash top)\backslash to(X,\backslash top)$ Since $\backslash top\text{'}$ is a morphism we must have $(x\; \backslash top\text{'}\; y)\; \backslash top\; (u\; \backslash top\text{'}\; z)\; =\; (x\; \backslash top\; u)\; \backslash top\text{'}\; (y\; \backslash top\; z)$ If we want to take the original operation, this will be allowed only if the medial identity $(x\; \backslash top\; y)\; \backslash top\; (u\; \backslash top\; z)\; =\; (x\; \backslash top\; u)\; \backslash top\; (y\; \backslash top\; z)$ is valid. This operation, which gives a medial magma, can have a two-sided identity only if it is a commutative monoidal operation. The ''if'' direction is obvious. As a result Med, the medial category, has all its objects as '' medial objects''; and this ''characterizes'' it. 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「Auto magma object」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.