Lemma 6.3.31. Let \(C\) be a stable \(\infty \)-category with a t-structure. Assume that \(C\) admits countable products and that \(C_{\geq 0}\) is closed under countable products. Then the t-structure is left complete if and only if it is left separated. Dually, if \(C\) admits countable coproducts and \(C_{\leq 0}\) is closed under countable coproducts, then the t-structure is right complete if and only if it is right separated.
Proof. This is [Lurie (2017), Proposition 1.2.1.19]. □
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