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In mathematics, and particularly category theory a coherence condition is a collection of conditions requiring that various compositions of elementary morphisms are equal. Typically the elementary morphisms are part of the data of the category. ==An illustrative example: a monoidal category== Part of the data of a monoidal category is a chosen morphism , called the ''associator'': for each triple of objects in the category. Using compositions of these , one can construct a morphism Actually, there are many ways to construct such a morphism as a composition of various . One coherence condition that is typically imposed is that these compositions are all equal. Typically one proves a coherence condition using a coherence theorem, which states that one only needs to check a few equalities of compositions in order to show that the rest also hold. In the above example, one only needs to check that, for all quadruples of objects , the following diagram commutes 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「coherence condition」の詳細全文を読む スポンサード リンク
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