Definition 6.4.6 (Ext-groups). Let \(C\) be a stable \(\infty \)-category. For objects \(X,Y \in C\) and \(n \in \Z \), we define the \(n\)-th Ext-group to be \[ \Ext ^n_C(X,Y) := \pi _{-n}\hom _C(X,Y) \simeq \pi _0 \Hom _C(X,Y[n]). \]
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