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In mathematics, especially homological algebra, a differential graded category or DG category for short, is a category whose morphism sets are endowed with the additional structure of a differential graded ''Z''-module. In detail, this means that , the morphisms from any object ''A'' to another object ''B'' of the category is a direct sum and there is a differential ''d'' on this graded group, i.e. for all ''n'' a linear map , which has to satisfy . This is equivalent to saying that is a cochain complex. Furthermore, the composition of morphisms is required to be a map of complexes, and for all objects ''A'' of the category, one requires . == See also == * Differential algebra * Graded (mathematics) * Graded category 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「differential graded category」の詳細全文を読む スポンサード リンク
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