Homological algebra | Categories in category theory

Differential graded category

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 . (Wikipedia).

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Related pages

Graded (mathematics) | Differential algebra | Derivator | Homological algebra | Stable homotopy category | Differential graded algebra | Smooth morphism | Additive category | Linear map | Graded category | Mathematics | Proper morphism | Field (mathematics) | Triangulated category | Ring (mathematics) | Category (mathematics) | Direct sum | Scheme (mathematics) | Derived category | Differential graded module | Model category