  We prove that the Drinfeld center of a fusion 2-category is invariant under
Morita equivalence. We go on to show that the concept of Morita equivalence
between connected fusion 2-categories recovers exactly the notion of Witt
equivalence between braided fusion 1-categories. A strongly fusion 2-category
is a fusion 2-category whose braided fusion 1-category of endomorphisms of the
monoidal unit is $\mathbf{Vect}$ or $\mathbf{SVect}$. We prove that every
fusion 2-category is Morita equivalent to the 2-Deligne tensor product of a
strongly fusion 2-category and an invertible fusion 2-category. We proceed to
show that every fusion 2-category is Morita equivalent to a connected fusion
2-category. As a consequence, we find that every rigid algebra in a fusion
2-category is separable. This implies in particular that every fusion
2-category is separable. Conjecturally, separability ensures that a fusion
2-category is 4-dualizable. We define the dimension of a fusion 2-category, and
prove that it is always non-zero. Finally, we show that the Drinfeld center of
any fusion 2-category is a finite semisimple 2-category.
