0NKR Proof. By proposition 4.11, we have natural equivalences N(Fun𝒮(𝒜op,𝒮)c)[W−1]ω≃Ψperf𝒜≃Funex(Ψtri𝒜op,𝒮∞)ω.\mathrm{N}(\mathrm{Fun}_{\mathcal{S}}({\mathcal{A}}^{\op},{\mathcal{S}})^{\mathrm{c}})[W^{-1}]^{\omega}\simeq\Psi_{\perf}{\mathcal{A}}\simeq\mathrm{Fun}^{\ex}(\Psi_{\tri}{\mathcal{A}}^{\op},{\mathcal{S}}_{\infty})^{\omega}. These allows us to identify the smallest stable subcategory Ψtri𝒜⊆Ψperf𝒜\Psi_{\tri}{\mathcal{A}}\subseteq\Psi_{\perf}{\mathcal{A}} spanned by the representable functors a^:𝒜op→𝒮\widehat{a}\colon{\mathcal{A}}^{\op}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{S}} with the stably representable functors Σ∞a^:Ψtri𝒜op→𝒮∞\Sigma^{\infty}\widehat{a}\colon\Psi_{\tri}{\mathcal{A}}^{\op}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{S}}_{\infty}. ∎