ScalingStacks

(8.4)

$$\Cone\left(\underline{{\mathcal{U}}_{\mathrm{add}}^{\kappa}}({\mathcal{A}})\longrightarrow\underline{{\mathcal{U}}_{\mathrm{add}}^{\kappa}}({\mathcal{B}})\right)\longrightarrow\underline{{\mathcal{U}}_{\mathrm{add}}^{\kappa}}({\mathcal{B}}/{\mathcal{A}})\,,$$

where ${\mathcal{A}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{B}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{B}}/{\mathcal{A}}$ is a strict-exact sequence in $\underline{{\mathcal{E}}_{\mathrm{wL}}^{\kappa}}$ (see section 5.5). Let $\underline{{\mathcal{U}}_{\mathrm{wloc}}^{\kappa}}$ be the following composite

$$\Cat_{\infty}^{\perf}\stackrel{{\scriptstyle\underline{{\mathcal{U}}_{\mathrm{add}}^{\kappa}}}}{{\longrightarrow}}\underline{{\mathcal{M}}_{\mathrm{add}}^{\kappa}}\stackrel{{\scriptstyle\gamma}}{{\longrightarrow}}\underline{{\mathcal{M}}_{\mathrm{wloc}}^{\kappa}}\,,$$

where $\gamma$ is the localization functor.