ScalingStacks

Theorem 1.9. Suppose $p:X\to Y$ is a map of perfect stacks that satisfies descent. Then there is a canonical equivalence

$$\mathcal{Z}(\qc(X\times_{Y}X))\simeq\qc({\mathcal{L}Y})$$

in which the central functor

$$\qc({\mathcal{L}Y})\simeq\mathcal{Z}(\qc(X\times_{Y}X))\to\qc(X\times_{Y}X)$$

is given by pullback and pushforward along the correspondence

$$\mathcal{L}Y\longleftarrow\mathcal{L}Y\times_{Y}X\longrightarrow X\times_{Y}X.$$