ScalingStacks

Let \(\mathcal C\) be a symmetric monoidal \(\infty\)-category with initial tensor unit and let \(X\) be an object in \(\mathcal C\) whose center \(\mathfrak{Z}(X) \in \mathrm{Alg}_{\mathbb E_1}(\mathcal C)\) exists. Then, the forgetful functor \[ \mathrm{Alg}_{\mathbb E_1}(\mathcal C)_{/\mathfrak{Z}(X)} \times_{\mathcal C_{/X}} \{ \mathrm{id}_X\} \rightarrow\mathrm{Alg}_{\mathbb E_1}(\mathcal C) \times_{\mathcal C} \{X\}\] is an equivalence of \(\infty\)-categories.