ScalingStacks

Definition 3.2. A derived stack $X$ is said to be perfect if it has affine diagonal and the $\infty$-category $\qc(X)$ is the inductive limit

$$\qc(X)\simeq\operatorname{Ind}\operatorname{Perf}(X)$$

of the full $\infty$-subcategory $\operatorname{Perf}(X)$ of perfect complexes.

A morphism $X\to Y$ is said to be perfect if its fibers $X\times_{Y}U$ over affines $U\to Y$ are perfect.