We use the following notation:
\(\mathrm{add}\) for the full \(\infty\)-subcategory of \(\mathrm{Cat}_{\infty}^{\sqcup, \mathrm{idem}}\) consisting of additive, idempotent complete, small \(\infty\)-categories.
\(\mathrm{st}\) for the full \(\infty\)-subcategory of \(\mathrm{Cat}_{\infty}^{\mathrm{rex}, \mathrm{idem}}\) consisting of stable, idempotent complete, small \(\infty\)-categories.