ScalingStacks

Definition 2.12. An $\infty$-category is stable [53, 1.1.1.9] if it has finite limits and colimits and pushout and pullback squares coincide [53, 1.1.3.4]. Let $\Cat_{\infty}^{\ex}$ denote the (pointed) $\infty$-category of small stable $\infty$-categories and exact functors (i.e., functors which preserve finite limits and colimits) [53, §1.1.4]. The $\infty$-category of exact functors between ${\mathcal{A}}$ and ${\mathcal{B}}$ is denoted by $\mathrm{Fun}^{\ex}({\mathcal{A}},{\mathcal{B}})$; this is the full $\infty$-subcategory of $\mathrm{Fun}({\mathcal{A}},{\mathcal{B}})$ spanned by the exact functors.