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On reflective subcategories of quasiabelian categories. (Russian. English summary) Zbl 1101.46325
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
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