ScalingStacks

Definition 3.1. Let $A$ be a derived commutative ring. An $A$-module $M$ is perfect if lies in the smallest $\infty$-subcategory of $\Mod_{A}$ containing $A$ and closed under finite colimits and retracts. For a derived stack $X$, $\infty$-category $\operatorname{Perf}(X)$ is the full $\infty$-subcategory of $\qc(X)$ consisting of those sheaves $M$ whose restriction $f^{*}M$ to any affine $f:U\rightarrow X$ over $X$ is a perfect module.