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We show that if a (not necessarily algebraic) triangulated category Tcontains an admissible hereditary abelian subcategory H, then we can lift theinclusion of H into T to a fully faithful triangle functor from the whole ofthe bounded derived category of H to T. This allows us prove, for example, thata triangulated category T is triangle equivalent to the bounded derivedcategory of an hereditary abelian category if and only if T admits a split,bounded t-structure.

Characterising the bounded derived category of an hereditary abelian category