Magnitude conjecture

MagnitudeConjecture.Algebra.RightModuleStandardFormARIncomingNonsplit

Nonsplitting of the recovered incoming map #

source
@[instance_reducible]
def MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.standardFormARIncomingNonsplitQuiver {k A : Type u} [Field k] [Ring A] [Algebra k A] [FiniteDimensional k A] [IsNoetherianRing Aᵐᵒᵖ] (S : FiniteIndecomposableSkeleton k A) :
Quiver (Fin S.n)
Instances For
    source
    @[instance_reducible]
    noncomputable def MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.standardFormARIncomingNonsplitArrowFintype {k A : Type u} [Field k] [Ring A] [Algebra k A] [FiniteDimensional k A] [IsNoetherianRing Aᵐᵒᵖ] (S : FiniteIndecomposableSkeleton k A) (x y : Fin S.n) :
    Fintype (x ⟶ y)
    Instances For
      source
      theorem MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.standardFormRecoveredIncomingMap_not_splitEpi {k A : Type u} [Field k] [IsAlgClosed k] [Ring A] [Algebra k A] [FiniteDimensional k A] [IsNoetherianRing Aᵐᵒᵖ] (S : FiniteIndecomposableSkeleton k A) (z : Fin S.n) :
      ¬CategoryTheory.IsSplitEpi (S.standardFormRecoveredIncomingMap z)

      The complete recovered incoming map is not a split epimorphism.