Irreducible spaces for the allowed-shift interval family #
noncomputable def
MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.standardFormIntervalFamily_irreducibleEquiv
{k A : Type u}
[Field k]
[IsAlgClosed k]
[Ring A]
[Algebra k A]
[FiniteDimensional k A]
[IsNoetherianRing Aᵐᵒᵖ]
(S : FiniteIndecomposableSkeleton k A)
(m : ℕ)
(a b : S.standardFormSupportedLabel m)
:
CategoricalIrreducible.Space k
((S.standardFormIntervalAlgebraEquivalence m).inverse.obj (S.standardFormSupportedFamily m a))
((S.standardFormIntervalAlgebraEquivalence m).inverse.obj (S.standardFormSupportedFamily m b)) ≃ₗ[k] CategoricalIrreducible.Space k (S.standardFormSupportedFamily m a) (S.standardFormSupportedFamily m b)
The quotient for the actual interval-module family is the quotient on its literal allowed-shift representatives in the supported category.