Kerodon

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

Example 1.4.2.14. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. If we refer to a commutative diagram $\sigma :$

\[ \xymatrix { & Y \ar [dr]^{g} & \\ X \ar [ur]^{f} \ar [rr]^{h} & & Z, } \]

then we mean that $\sigma $ is a $2$-simplex of $\operatorname{\mathcal{C}}$ satisfying $d_0(\sigma ) = g$, $d_1(\sigma ) =h$, and $d_2(\sigma ) = f$. In other words, we mean that $\sigma $ is a $2$-simplex which witnesses $h$ as a composition of $f$ and $g$, in the sense of Definition 1.3.4.1.