Remark 6.3.25. In the context of homological algebra, for example when \(C\) is the derived \(\infty \)-category of an abelian category, the objects \(\pi _n(X)\) are often denoted by \(H_n(X)\) instead, emphasizing the analogy with the homology groups of a chain complex rather than the analogy with homotopy groups of a spectrum. Under the equivalence \(\D (\Aa )^{\heartsuit } \simeq \Aa \) from Example 6.3.20, the object \(\pi _n(A) \in \Aa \) agrees with the \(n\)-th homology \(H_n(A)\) of \(A\) viewed as a chain complex.
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