t-structure on modules over nonconnective algebras

Remark 8.2.11. The \(\infty \)-category \(\LMod _R\) also admits a t-structure when \(R\) is not connective. In this case, the subcategory \(\LMod _{R,\geq 0}\) may still be described as the smallest subcategory of \(\LMod _R\) that contains \(R\) and is closed under colimits. The subcategory \(\LMod _{R,\leq 0}\) is still given by those \(R\)-modules whose underlying spectrum is coconnective. We refer to [Lurie (2017), Proposition 1.4.4.11] for a very general result for producing t-structures on presentable \(\infty \)-categories.