category with duals (list of them)
dualizable object (what they have)
Let be an (∞,n)-category. We say that
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).
For more see at (infinity,n)-category with adjoints.