Definition 6.2.6. Let \(\Aa \) be an abelian category. We define the \(\infty \)-category \(\Kk (\Aa )\) as the localization \[ \Kk (\Aa ) \quad := \quad \Ch (\Aa )[\{\text {chain homotopy equivalences}^{-1}\}]. \] There are localization functors \(\Ch (\Aa ) \to \Kk (\Aa ) \to \D (\Aa )\).
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