Homotopy-group objects for a t-structure

Definition 6.3.24. Let \(C\) be a stable \(\infty \)-category equipped with a t-structure and let \(X\) be an object of \(C\). For every \(n \in \Z \), we define the \(n\)-th homotopy group object \(\pi _n(X) \in C^{\heartsuit }\) by \begin {align*} \pi _n(X) := \tau _{\geq 0} \tau _{\leq 0} (X[-n]) \qin C^{\heartsuit }. \end {align*}