Definition 4.1.1 (Pointed \(\infty \)-category). We call an \(\infty \)-category \(C\) pointed if it has a zero object, i.e. an object \(0\) that is both initial and terminal (Definition 1.7.7). Given objects \(X,Y \in C\), we define the null map \(0\colon X \to Y\) as the composite of the unique maps \(X \to 0\) and \(0 \to Y\).
A functor \(F\colon C \to D\) between pointed \(\infty \)-categories is called pointed if it preserves zero objects.
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