Kerodon

Notation 10.2.2.2. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We will often use the notation $X_{\bullet }$ to indicate a semisimplicial object of $\operatorname{\mathcal{C}}$. In this case, we write $X_{n}$ for the value of the functor $X_{\bullet }$ on the object $[n] \in \operatorname{{\bf \Delta }}^{\operatorname{op}}_{\operatorname{inj}}$. Similarly, we often use an expression like $X^{\bullet }$ to indicate a cosemisimplicial object of $\operatorname{\mathcal{C}}$, and $X^{n}$ for its value on the object $[n] \in \operatorname{{\bf \Delta }}_{\operatorname{inj}}$.