Following definition 3.2.3, we use the following notations:
\({\mathrm{Pr}^{\mathrm{L}}_{\mathrm{st}}}\) for the full subcategory of \(\mathrm{Pr}^\mathrm{L}\) on the stable, presentable \(\infty\)-categories and \({\mathrm{Pr}^{\mathrm{L}}_{\mathrm{add}}}\) for the full subcategory on the additive, presentable \(\infty\)-categories.
\(\mathrm{Pr}^{\mathrm{L}, \mathrm{c}}_{\mathrm{st}}\) for the full subcategory of \(\mathrm{Pr}^{\mathrm{L},\mathrm{c}}\) on the stable presentable \(\infty\)-categories which are compactly generated as \(\infty\)-categories, and \(\mathrm{Pr}^{\mathrm{L}, \mathrm{cp}}_{\mathrm{add}}\) for the full subcategory of \(\mathrm{Pr}^{\mathrm{L},\mathrm{cp}}\) on the additive presentable \(\infty\)-categories which are projectively generated as \(\infty\)-categories.