О рефлективных подкатегориях полуабелевых категорий

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 subcategory of quasiabelian category and develop a version of “relative homological algebra” for such subcategories.