  We define a notion of grading of a monoid T in a monoidal category C,
relative to a class of morphisms M (which provide a notion of M-subobject). We
show that, under reasonable conditions (including that M forms a factorization
system), there is a canonical grading of T. Our application is to graded monads
and models of computational effects. We demonstrate our results by
characterizing the canonical gradings of a number of monads, for which C is
endofunctors with composition. We also show that we can obtain canonical grades
for algebraic operations.
