ScalingStacks

Proof. It suffices to show that the forgetful functor $\disk_{n/M}^{B}\rightarrow\disk_{n/M}$ is an equivalence. By definition, this functor is the projection from the double overcategory:

$$\disk_{n/M}^{B}~:=~(\disk_{n/B})_{/M}\longrightarrow\disk_{n/M}.$$

This functor is a pullback of the likewise functor $\bigl((\spaces_{/\BTop(n)})_{/B}\bigr)_{/M}\to(\spaces_{/\BTop(n)})_{/M}$, which is an equivalence by Lemma 2.5.

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