dg category

Summary

A dg category, or differential graded category, is a category whose morphism sets are chain complexes and whose composition is compatible with the differentials. It is a category enriched over chain complexes of modules over a commutative ring. Dg categories serve as enhancements of triangulated categories: they keep homotopical information that the triangulated category loses, such as functorial cones. They are a main tool in noncommutative algebraic geometry and in the study of derived categories of sheaves.