1994/01/01 by Bernhard Keller · 7 citations
Mathematics · #2-category #Abelian category #Abelian group #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Biproduct #Category of groups #Category theory #Context (archaeology) #Derived category #Formalism (music) #Functor #Homological algebra #Homotopy and Cohomology in Algebraic Topology #Mathematics #Morita therapy #Pure mathematics #Triangulated category
paper · pdf · doi:10.24033/asens.1689
openalex publication_date 1994/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14
We investigate the (unbounded) derived category of a differential Z-graded category (=DG category). As a first application, we deduce a "triangulated analogue" (4.3) of a theorem of Freyd's [5], Ex. 5.3 H, and Gabriel's [6], Ch. V, characterizing module categories among abelian categories. After adapting some homological algebra we go on to prove a "Morita theorem" (8.2) generalizing results of [19] and [20]. Finally, we develop a formalism for Koszul duality