Example 6.3.20 (Heart of the standard t-structure). Let \(\Aa \) be an abelian category. The heart of the standard t-structure on \(\D (\Aa )\) is equivalent to \(\Aa \). Indeed, the heart consists of those complexes whose homology is concentrated in degree zero, which by Proposition 6.1.26 is precisely the essential image of the fully faithful functor \(\Aa \hookrightarrow \D (\Aa )\).
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