We apply the theory of the derived category of exact categories to the category G-Ban of Banach modules over the discrete group G. Since there are enough injectives in G-Ban, right derived functors exist. The heart of the canonical t-structure on the derived category D(Ban) is equivalent to Waelbroeck's Abelian category qBan of quotient Banach spaces. The right derived functor of the functor "submodule of G-invariant vectors" yields a universal delta-functor with values in qBan which allows us to reconstruct the bounded cohomology functors in the sense of Gromov-Brooks-Ivanov-Noskov.
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