ScalingStacks

Definition 2.1.4. Let $F\colon\mathcal{C}\to\mathcal{D}$ be a functor between $\infty$-categories. We say that an object $Y$ is reduced if $F\left(Y\right)$ is initial in $\mathcal{D}$. We define $\mathcal{C}^{\operatorname{\scriptsize{red}}}$ to be the full subcategory of $\mathcal{C}$ spanned by the reduced objects ($F$ will always be clear from the context when we employ this terminology).