Notation 7.6.3.11 (Fiber Products). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, and suppose we are given a pair of morphisms $f_0: X_0 \rightarrow X$ and $f_1: X_1 \rightarrow X$ of $\operatorname{\mathcal{C}}$ having the same target. It follows from Proposition 7.1.1.12 that if there exists a pullback diagram
in $\operatorname{\mathcal{C}}$, then the object $X_{01}$ is determined up to isomorphism by $f_0$ and $f_1$. To emphasize this, we will often denote the object $X_{01}$ by $X_0 \times _{X} X_1$ and refer to it as the fiber product of $X_0$ with $X_1$ over $X$. Similarly, if there exists a pushout diagram
in $\operatorname{\mathcal{C}}$, then the object $Y_{01}$ is determined up to isomorphism by $g_0$ and $g_1$. To emphasize this, we often denote the object $Y_{01}$ by $Y_{0} {\coprod }_{ Y} Y_1$ and refer to it as the pushout of $Y_0$ with $Y_1$ along $Y$.