ScalingStacks

Corollary 4.12. Let $X$ be a perfect stack, and let $\Sigma$ be a finite simplicial set. Then there is canonical equivalence

$$\qc(X^{\Sigma})\simeq\qc(X)\otimes\Sigma.$$

In other words, the $\infty$-category of sheaves on the mapping stack is calculated as the tensor product of the $\infty$-categories of sheaves on the simplices.