Definition 8.2.2. Let \(C\) be a stable \(\infty \)-category equipped with a t-structure and a connectivity-preserving symmetric monoidal structure. Let \(R \in \Alg (C_{\geq 0})\) be a connective associative algebra in \(C\). We say that a left \(R\)-module \(M\) is connective if its underlying object in \(C\) is connective, and similarly for coconnective modules. This defines full subcategories \[ \LMod _R(C)_{\geq 0}, \quad \LMod _R(C)_{\leq 0} \quad \subseteq \quad \LMod _R(C). \]
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