2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154846We construct an A_infinity-category D(C|B) from a given A_infinity-category C and its full subcategory B. The construction is similar to a particular case of Drinfeld's quotient of differential graded categories. We use D(C|B) to construct an A_infinity-functor of K-injective resolutions of a complex. The conventional derived category is obtained as the 0-th cohomology of the quotient of differential graded category of complexes over acyclic complexes.49 pages, LaTeX, uses Paul Taylor's diagrams.tex. Close to published versionCategory TheoryK-Theory and HomologyQuantum Algebratext