Uniqueness of shifts of actual graded modules #
theorem
MagnitudeConjecture.Graded.FiniteGradedModule.shift_eq_of_iso
{k A : Type u}
[Field k]
[Ring A]
[Algebra k A]
{R : VectorGrading k A}
(X : FiniteGradedModule R)
[Nontrivial ↑X.module]
(s t : ℤ)
(e : { obj := X, degree := s } ≅ { obj := X, degree := t })
:
s = t
Distinct shifts of a nonzero finite-dimensional graded module are not isomorphic by homogeneous degree-preserving maps.