ScalingStacks

Axiom (C.5: Versality). For any $\infty$-category $\mathcal{D}$ and any fully faithful functor $g\colon\gaunt_{n}^{\omega}\hookrightarrow\mathcal{D}$ satisfying Axioms C.1–4, there exist a left adjoint $K\colon\mathcal{C}\to\mathcal{D}$ and a natural transformation $\xi\colon K\circ f\to g$ such that $\xi|_{\mathbb{G}_{n}}\colon K\circ f|_{\mathbb{G}_{n}}\to g|_{\mathbb{G}_{n}}$ is an equivalence.