Lemma 6.3.26. Let \(F\colon C \to D\) be a t-exact functor between two stable \(\infty \)-categories equipped with t-structures. Then for all \(X \in C\) and \(n \in \Z \), there is a natural isomorphism \(F(\pi _n X) \iso \pi _n F(X)\).
Proof. By Lemma 6.3.13 we have natural isomorphisms \[ F(\pi _n X) = F(\tau _{\geq 0} \tau _{\leq 0}(X[-n])) \iso \tau _{\geq 0} \tau _{\leq 0} (F(X)[-n]) = \pi _n(F(X)). \qedhere \] □
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