Dimension shifting for a coherent defect #
This leaf specializes the generic projective-middle dimension shift to the right half of the four-term representable resolution of a coherent defect.
noncomputable def
MagnitudeConjecture.RightModule.FiniteIndecomposableSkeleton.finiteContravariantDefectDimensionShiftLinearEquiv
{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.FiniteContravariantFunctor]
{K : CategoryTheory.ShortComplex FG}
(hK : K.ShortExact)
(X : S.IndecCategory)
:
CategoryTheory.Abelian.Ext (S.finiteContravariantDefectSyzygy K) (S.finiteContravariantRepresentableOnSkeleton.obj X)
1 ≃ₗ[k] CategoryTheory.Abelian.Ext (S.finiteContravariantDefect K) (S.finiteContravariantRepresentableOnSkeleton.obj X) 2
Dimension shifting across the right half of the four-term representable resolution.