ScalingStacks

Definition 2.16. Let $\mathcal{C}$ be an $\infty$-category. Then we will say that a functor $X\colon\mathcal{C}^{\op}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{S}}_{\infty}$ is stably representable if there exists a spectrum object $A\in\mathrm{Sp}(\mathcal{C}_{*})$ and an equivalence $\mathrm{Map}(-,A)\simeq X$, where $\mathrm{Map}(-,A)$ denotes the functor $\mathcal{C}^{\op}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{S}}_{\infty}$ represented by $A$ via the spectral Yoneda embedding $\mathrm{Sp}(\mathcal{C}_{*})\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\mathrm{Fun}(\mathcal{C}^{\op},{\mathcal{S}}_{\infty})$.