ScalingStacks

Definition 5.28. An exact sequence of small stable $\infty$-categories of the form

(5.29)

$${\mathcal{A}}\longrightarrow{\mathcal{B}}\longrightarrow{\mathcal{B}}/{\mathcal{A}}$$

is called strict-exact if ${\mathcal{A}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{B}}$ is the inclusion of a full subcategory and any object of ${\mathcal{B}}$ which is a summand of an object of ${\mathcal{A}}$ is also in ${\mathcal{A}}$. In particular, every split-exact sequence (see definition 5.18) is equivalent to a strict-exact exact sequence.