Is there any reason why this is true? I haven't found any proof yet.
I know what triangulated categories and t-structures are, however I'm not convinced that hearts of t-structures are abelian categories.
2026-04-07 03:59:13.1775534353
Why are hearts of t-structures of triangulated categories abelian?
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I understand your question as being a reference request.
This is a theorem first proved in Beilinson, Bernstein and Deligne's paper Faisceaux pervers, published in Astérisque. The result in question is Théorème 1.3.6.
A proof in English appears in Kashiwara and Schapira's book Sheaves on manifolds, published by Springer. The result is Proposition 10.1.11.