Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Definition 1.3.4.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Suppose we are given objects $X,Y,Z \in \operatorname{\mathcal{C}}$ and morphisms $f: X \rightarrow Y$, $g: Y \rightarrow Z$, and $h: X \rightarrow Z$. We will say that $h$ is a composition of $f$ and $g$ if there exists a $2$-simplex $\sigma $ of $\operatorname{\mathcal{C}}$ satisfying $d_0(\sigma ) = g$, $d_1(\sigma ) = h$, and $d_2(\sigma ) = f$. In this case, we will also say that the $2$-simplex $\sigma $ witnesses $h$ as a composition of $f$ and $g$.