  The classical Morita Theorem for rings established the equivalence of three
statements, involving categorical equivalences, isomorphisms between corners of
finite matrix rings, and bimodule homomorphisms. A fourth equivalent statement
(established later) involves an isomorphism between infinite matrix rings. In
our main result, we establish the equivalence of analogous statements involving
graded categorical equivalences, graded isomorphisms between corners of finite
matrix rings, graded bimodule homomorphisms, and graded isomorphisms between
infinite matrix rings.
