Yoneda lifting for the standard-form mesh resolution

The reflected raw relation is lifted through mesh exactness. This final stage is kept separate from the expensive Yoneda calculation.

@[instance_reducible]

def MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.standardFormMeshYonedaLiftQuiver {k A : Type u} [Field k] [Ring A] [Algebra k A] [FiniteDimensional k A] [IsNoetherianRing Aᵐᵒᵖ] (S : FiniteIndecomposableSkeleton k A) : Quiver (Fin S.n)

@[instance_reducible]

noncomputable def MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.standardFormMeshYonedaLiftArrowFintype {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)

theorem MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.standardFormSimpleResolution_yoneda_lift {k A : Type u} [Field k] [IsAlgClosed k] [Ring A] [Algebra k A] [FiniteDimensional k A] [IsNoetherianRing Aᵐᵒᵖ] (S : FiniteIndecomposableSkeleton k A) (hP : S.standardFormRightMeshData.FiniteContravariantRepresentables) (z : { z : Fin S.n // z ∉ S.standardFormProjectiveSet }) (x : Fin S.n) (h : S.standardFormRightMeshData.incomingCoefficientFiniteModule hP ↑z ⟶ S.standardFormRightMeshData.contravariantRepresentableFiniteModule hP x) (hh : CategoryTheory.CategoryStruct.comp (S.standardFormRightMeshData.translationMapFinite hP z) h = 0) : ∃ (t : MeshCategory.obj S.standardFormRightMeshData ↑z ⟶ MeshCategory.obj S.standardFormRightMeshData x), ∀ (a : MeshCategory.RightMeshData.IncomingArrow ↑z), (S.standardFormSimpleResolutionYonedaCoefficient hP z x h a).hom = CategoryTheory.CategoryStruct.comp (S.standardFormRightMeshData.incomingArrowHom a) t

A morphism out of the incoming coefficient module which kills the translation map is induced by a single morphism in the mesh category.