ScalingStacks

Given a functor \(H \colon \mathcal B\rightarrow\mathcal C\) of \(\infty\)-categories and a commuting square of \(\infty\)-categories Assume that for any \(b_0, b_1 \in \mathcal B\) in the image of \(\{0\} \times \mathcal A\rightarrow S^0 \times \mathcal A\rightarrow\mathcal B\) and \(\{1\} \times \mathcal A\rightarrow S^0 \times \mathcal A\rightarrow\mathcal B\), respectively, and any commuting square the space of dashed lifts is contractible. Then, the space of lifts of the square ([00GE]) is contractible.