0NM9 Definition 5.19. A sequence πββ¬βπ{\mathcal{A}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{B}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{C}} of spectral categories is exact if the induced sequence of stable presentable β\infty-categories Nβ‘(Ξ©ββModβ(π)cf)βΆNβ‘(Ξ©ββModβ(β¬)cf)βΆNβ‘(Ξ©ββModβ(π)cf)\mathrm{N}(\Omega^{\infty}\Mod({\mathcal{A}})^{\cf})\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\mathrm{N}(\Omega^{\infty}\Mod({\mathcal{B}})^{\cf})\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\mathrm{N}(\Omega^{\infty}\Mod({\mathcal{C}})^{\cf}) is exact.