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Balanced pairs induce recollements

ABSTRACT Let 𝒜 be an abelian category with arbitrary (set-indexed) coproducts and exact products. Let (𝒫,ℐ) be a complete balanced pair. Then as in the classical case, we prove that there exists a recollement with the middle term K(𝒜), the homotopy category of 𝒜. In particular, this implies that the relative derived category exists. Two applications are given.