ScalingStacks

Corollary 6.7. For $X$ a perfect stack, the center $\mathcal{T}r(\qc(X))\simeq\qc(\mathcal{L}X)$ has the structure of a stable framed $\mathcal{E}_{2}$-category. For a map $X\to Y$ of perfect stacks, the same holds for the center $\mathcal{T}r(\qc(X\times_{Y}X))\simeq\qc(\mathcal{L}X)$.