Dimension shifting for a covariant coherent defect #
noncomputable def
MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.finiteCovariantDefectDimensionShiftLinearEquiv
{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 : S.IndecCategoryᵒᵖ)
:
CategoryTheory.Abelian.Ext (S.finiteCovariantDefectSyzygy K) (S.finiteCovariantRepresentableOnSkeleton.obj X) 1 ≃ₗ[k] CategoryTheory.Abelian.Ext (S.finiteCovariantDefect K) (S.finiteCovariantRepresentableOnSkeleton.obj X) 2
Dimension shifting across the right half of the covariant representable resolution.