The Stacks project

Definition 4.27.4. Let $\mathcal{C}$ be a category and let $S$ be a left multiplicative system of morphisms of $\mathcal{C}$. Given any morphism $f : X \to Y'$ in $\mathcal{C}$ and any morphism $s : Y \to Y'$ in $S$, we denote by $s^{-1} f$ the equivalence class of the pair $(f : X \to Y', s : Y \to Y')$. This is a morphism from $X$ to $Y$ in $S^{-1} \mathcal{C}$.