Kerodon

Notation 1.4.4.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f: X \rightarrow Y$ and $g: Y \rightarrow Z$ be a pair of morphisms in $\operatorname{\mathcal{C}}$. We will write $h = g \circ f$ to indicate that $h$ is a composition of $f$ and $g$ (in the sense of Definition 1.4.4.1). In this case, it should be implicitly understood that we have chosen a $2$-simplex that witnesses $h$ as a composition of $f$ and $g$. We will sometimes abuse terminology by referring to $h$ as the composition of $f$ and $g$. However, the reader should beware that only the homotopy class of $h$ is well-defined (Proposition 1.4.4.2).