We denote by
\(\mathrm{Pr}^\mathrm{L}\) the \(\infty\)-category of presentable \(\infty\)-categories and small colimit preserving functors, i.e left adjoint functors by the adjoint functor theorem.
\(\mathrm{Fun^L}(\mathcal C,\mathcal D)\), for \(\mathcal C, \mathcal D\in \mathrm{Pr}^\mathrm{L}\), the full subcategory of \(\mathrm{Fun}(\mathcal C, \mathcal D)\) of left adjoint (equivalently cocontinuous) functors. Dually, full subcategories of right adjoint functors will be denoted \(\mathrm{Fun^R}(-,-)\).
When denoting an adjunction
between \(\infty\)-categories, we use the convention that the top arrow is the left adjoint and the bottom arrow the right adjoint.