  We define for each $n \geq 1$ a symmetric monoidal $(\infty, n+1)$-category
$n\mathrm{Pr}^L$ whose objects we call presentable $(\infty,n)$-categories,
generalizing the usual theory of presentable $(\infty,1)$-categories. We show
that each object $\mathcal{C}$ in $n\mathrm{Pr}^L$ has an underlying
$(\infty,n)$-category $\psi_n(\mathcal{C})$ which admits all conical colimits,
and that conical colimits of right adjointable diagrams in
$\psi_n(\mathcal{C})$ can be computed in terms of conical limits after passage
to right adjoints.
