  We consider algebras and Frobenius algebras, internal to a monoidal category,
that are graded over a finite abelian group. For the case that A is a twisted
group algebra in a linear abelian monoidal category we obtain a graded
generalization of the Schur Lemma for the category of induced A-modules. We
further show that if the monoidal category is braided and A is commutative up
to a bicharacter of the grading group, then the category of induced A-modules
can be endowed with a graded-monoidal structure that is twisted by the
bicharacter. In the particular case that the grading group is Z/2Z, these
findings reproduce known results about superalgebras and super-monoidal
structures.
