  We develop the Morita theory of fusion 2-categories. In order to do so, we
begin by proving that the relative tensor product of modules over a separable
algebra in a fusion 2-category exists. We use this result to construct the
Morita 3-category of separable algebras in a fusion 2-category. Then, we go on
to explain how module 2-categories form a 3-category. After that, we define
separable module 2-categories over a fusion 2-category, and prove that the
Morita 3-category of separable algebras is equivalent to the 3-category of
separable module 2-categories. As a consequence, we show that the dual tensor
2-category with respect to a separable module 2-category, that is the
associated 2-category of module 2-endofunctors, is a multifusion 2-category.
Finally, we give three equivalent characterizations of Morita equivalence
between fusion 2-categories.
