Let C be an additive category in which each morphism has a kernel. It is proved that the homotopy category of the category of complexes over C which are concentrated in degrees 2, 1, 0 and are exact in degrees 2 and 1 is Abelian. Under assumption that a category C is Abelian, this result was obtained earlier by considering the heart of a suitable t-structure on the homotopy category of C.
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