The zero object and null maps in pointed animae

Notation 2.4.3. The one-point anima \(*\) is canonically pointed; we denote the corresponding pointed anima by \(0 \in \An _*\) and call it the zero object. One can show it is both initial and terminal in \(\An _*\): given pointed animae \(X,Y \in \An _*\), there are unique morphisms \(X \to 0\) and \(0 \to Y\). (See Lemma 4.1.9 for more details.) We denote their composite by \[ 0\colon X \to Y \] and call it the null map.