Definition 6.5.11. Let \(N \in D^{\heartsuit }\) be an object in the heart of \(D\). A flat resolution of \(N\) is a long exact sequence \[ \dots \to F_2 \to F_1 \to F_0 \twoheadrightarrow N \to 0 \] in \(D^{\heartsuit }\) such that each object \(F_n\) is t-flat.
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