Lyubashenko, V. V.; Ovsienko, S. A. Category of \(A_{\infty}\)-categories and derived categories. (English) Zbl 1067.55500 Nauk. Zap., Kyïv 2003, No. 21, 5-20 (2003). 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. Cited in 1 Document MSC: 55U40 Topological categories, foundations of homotopy theory 18E30 Derived categories, triangulated categories (MSC2010) Keywords:category; transformation PDFBibTeX XMLCite \textit{V. V. Lyubashenko} and \textit{S. A. Ovsienko}, Nauk. Zap., Kyïv 2003, No. 21, 5--20 (2003; Zbl 1067.55500)