ScalingStacks

Proposition 6.5. For any perfect stack $X$, there is a symmetric monoidal functor

$$S_{X}:{\rm Bord}_{\rm Spaces}\to{\rm Cat}_{\infty}^{\rm ex}$$

with $S_{X}(U)=\qc(X^{U})$ and $S_{X}(T:U\to V)$ the functor $\qc(U)\to\qc(V)$ given by pullback and pushforward along the correspondence

$$X^{U}\leftarrow X^{T}\rightarrow X^{V}.$$