Objects and morphisms in Segal animae

Convention 24.1.3. Given a Segal anima \(X\), we refer to \(0\)-simplices \(x \in X_0\) as objects of \(X\), and to 1-simplices \(f\in X_1\) as morphisms of \(X\). We use the notation \(f\colon x \to y\) when \(d_1(f) \simeq x\) and \(d_0(f) \simeq y\). Given objects \(x,y \in X_0\), we define the hom anima in \(X\) as the following pullback:

We will sometimes refer to 2-simplices as homotopies.