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About: Differential graded category

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In mathematics, especially homological algebra, a differential graded category, often shortened to dg-category or DG category, is a category whose morphism sets are endowed with the additional structure of a differential graded -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 each n there is a linear map ,

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  • In mathematics, especially homological algebra, a differential graded category, often shortened to dg-category or DG category, is a category whose morphism sets are endowed with the additional structure of a differential graded -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 each n there is 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 . (en)
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  • In mathematics, especially homological algebra, a differential graded category, often shortened to dg-category or DG category, is a category whose morphism sets are endowed with the additional structure of a differential graded -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 each n there is a linear map , (en)
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  • Differential graded category (en)
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