Presentation-level reverse comparison naturality

theorem MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.finiteCovariantDefectPresentationLinearEquiv_representable_precomp {k A : Type u} [Field k] [IsAlgClosed k] [Ring A] [Algebra k A] [FiniteDimensional k A] [IsNoetherianRing Aᵐᵒᵖ] (S : FiniteIndecomposableSkeleton k A) [CategoryTheory.HasExt S.FiniteCovariantFunctor] {K : CategoryTheory.ShortComplex FG} (hK : K.ShortExact) {X Y : S.IndecCategoryᵒᵖ} (a : X ⟶ Y) (f : (S.fgObj (Opposite.unop X)).obj ⟶ K.X₃.obj) : (S.finiteCovariantDefectPresentationLinearEquiv hK Y) (Submodule.Quotient.mk (S.finiteRestrictedCovariantRepresentableMap (CategoryTheory.ObjectProperty.homMk (CategoryTheory.CategoryStruct.comp (S.fgMap a.unop).hom f)))) = ((CategoryTheory.Abelian.Ext.mk₀ (S.finiteCovariantRepresentableOnSkeleton.map a)).postcompOfLinear k (S.finiteCovariantDefect K) ⋯) ((S.finiteCovariantDefectPresentationLinearEquiv hK X) (Submodule.Quotient.mk (S.finiteRestrictedCovariantRepresentableMap (CategoryTheory.ObjectProperty.homMk f))))

Naturality of the reverse Ext² comparison on quotient representatives coming from restricted covariant Yoneda.