Definition 6.4.12. Let \(C\) be a stable \(\infty \)-category equipped with a t-structure, and let \(M \in C^{\heartsuit }\) be an object in the heart of \(C\). A projective resolution of \(M\) is a long exact sequence \[ \dots \to P_2 \to P_1 \to P_0 \twoheadrightarrow M \to 0 \] in \(C^{\heartsuit }\) such that each object \(P_n\) is t-projective.
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