n-category = (n,n)-category
n-groupoid = (n,0)-category
category with duals (list of them)
dualizable object (what they have)
Let be an (∞,n)-category. We say that
has adjoints if it has adjoints for k-morphisms with .
If is in addition a symmetric monoidal (∞,n)-category we say that
Finally we say that
This is (Lurie, def. 2.3.13, def. 2.3.16).