category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
monoidal dagger-category?
homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
n-category = (n,n)-category
n-groupoid = (n,0)-category
The coherence theorem for symmetric monoidal bicategories, like many coherence theorems, has several forms (or, alternatively, refers to several different theorems):
Every diagram of constraint 2-cells in a free symmetric monoidal bicategory commutes; in other words, any two parallel composites of constraint 2-cells are equal. Moreover, two parallel composites of constraint 1-cells are isomorphic if and only if they have the same underlying permutation, in which case they are uniquely isomorphic.
Every symmetric monoidal bicategory is equivalent to a strict symmetric monoidal bicategory.