Glotko, N. V.; Kuz’minov, V. I. On reflective subcategories of quasiabelian categories. (Russian. English summary) Zbl 1101.46325 Sib. Èlektron. Mat. Izv. 2, 68-78 (2005). Summary: We discuss some category-theoretical and homological aspects of functional analysis. We consider a pair consisting of a quasiabelian category and its full reflective subcategory. We introduce notions of reduced and nonreduced cohomologies for complexes in reflective subcategories of quasiabelian categories and develop a version of ‘relative homological algebra’ for such subcategories. MSC: 46M18 Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) 18G50 Nonabelian homological algebra (category-theoretic aspects) 18E10 Abelian categories, Grothendieck categories Keywords:universal square; co-universal square; commutative diagram PDFBibTeX XMLCite \textit{N. V. Glotko} and \textit{V. I. Kuz'minov}, Sib. Èlektron. Mat. Izv. 2, 68--78 (2005; Zbl 1101.46325) Full Text: EuDML