Presentable $(\infty ,n)$-categories

Abstract

We define for each $n\ge 1$ 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.

References in corpus (1)

• Higher Topos Theory