A counterexample to Raikov's conjecture

Quasi-abelian categories are additive categories for which the class of all short exact sequences defines an exact structure. Such categories are ubiquitous and form a natural framework for relative homological algebra and K-theory. Higher Ext-groups also exist in categories with the formally weaker property to be semi-abelian. Raikov's conjecture states that both concepts are equivalent. We use a tilted algebra of type (6) to construct a counterexample.