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Category of \(A_{\infty}\)-categories and derived categories. (English) Zbl 1067.55500

Summary: We define natural \(A_{\infty}\)-transformations and construct the \(A_{\infty}\)-category of \(A_{\infty}\)-functors. The notion of strict units in an \(A_{\infty}\)-category is made weaker. The 2-category of \(A_{\infty}\)-categories, functors and transformations is described. We study the quotient of an \(A_{\infty}\)-category over a full subcategory. The conventional derived category is obtained as the \(0\)-th cohomology of the quotient of differential graded category of complexes over acyclic complexes.

MSC:

55U40 Topological categories, foundations of homotopy theory
18E30 Derived categories, triangulated categories (MSC2010)
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