AlgebraicCurves.Cohomology.Proofs.ProjectiveCechBaseChange.S32F2.E_dP
Source context 12 commands
Surrounding namespaces, section variables, and local commands at this declaration.
section ProofImplementation
namespace AlgebraicCurves.Cohomology.Proofs.ProjectiveCechBaseChange
attribute [-instance] AlgebraicGeometry.OModulePresheaf.instSubsingletonObjZero
AlgebraicGeometry.OModulePresheaf.Leray.relAltC_scalarTower
AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_modΓ
AlgebraicGeometry.OModulePresheaf.Leray.relAltC_modΓ
AlgebraicGeometry.OModulePresheaf.Leray.biC_abGrp
AlgebraicGeometry.OModulePresheaf.Leray.relAltH_modΓ
AlgebraicGeometry.OModulePresheaf.Leray.ker_relAltd_smul
AlgebraicGeometry.OModulePresheaf.Leray.relAltH_scalarTower
AlgebraicGeometry.OModulePresheaf.Leray.relAltH_smul
AlgebraicGeometry.OModulePresheaf.Leray.biC_module
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instDecidableEqIdx
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintype
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instLinearOrder
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.instFintypeIdx DoubleComplex.instModuleE₂I
DoubleComplex.Bounded.modR DoubleComplex.instModuleE₂II DoubleComplex.instAddCommGroupE₂II
DoubleComplex.Bounded.abGrp DoubleComplex.instAddCommGroupE₂I
AlgebraicGeometry.ChowDatum.hι_closed AlgebraicGeometry.ChowDatumProj.hιN_closed
AlgebraicGeometry.ChowDatumProj.hp_proper AlgebraicGeometry.ChowDatum.hp_isoU
AlgebraicGeometry.ChowDatum.hp_proper AlgebraicGeometry.ProjSpace.algebraAway
AlgebraicGeometry.ProjSpace.instIsProperProdOverπ AlgebraicGeometry.ChowDatumProj.hp_isoU
AlgebraicGeometry.ProjSpace.isProper_π AlgebraicGeometry.ProjSpace.finiteType_mvPolynomial
ProjSpaceCech.GradedModule.H.module ProjSpaceCech.GradedModule.H.addCommGroup
ProjSpaceCech.GradedModule.sec.instAdd ProjSpaceCech.GradedModule.sec.instNeg
ProjSpaceCech.GradedModule.acg ProjSpaceCech.GradedModule.Frac.setoid
ProjSpaceCech.GradedModule.modR ProjSpaceCech.GradedModule.sec.instModule
ProjSpaceCech.GradedModule.sec.instAddCommGroup ProjSpaceCech.GradedModule.sec.instZero
attribute [-instance] ProjSpaceCech.GradedModule.Presentation.fJ
ProjSpaceCech.GradedModule.sec.instSMul ProjSpaceCech.Twist.H.module
ProjSpaceCech.Idx.instFintype ProjSpaceCech.Twist.H.addCommGroup
ProjSpaceCech.Idx.instDecidableEq ProjSpaceCech.Twist.Mon.instDecidableEq
ProjSpaceCech.Twist.cochain.instAddCommGroup ProjSpaceCech.Twist.cochain.instModule
attribute [-simp] AlgebraicGeometry.OModulePresheaf.prod_obj
AlgebraicGeometry.OModulePresheaf.restrOpen_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.injEq
AlgebraicGeometry.OModulePresheaf.pushforward_obj AlgebraicGeometry.OModulePresheaf.im_obj
AlgebraicGeometry.OModulePresheaf.pow_obj AlgebraicGeometry.OModulePresheaf.fstHom_app
AlgebraicGeometry.OModulePresheaf.ker_obj AlgebraicGeometry.OModulePresheaf.coker_obj
AlgebraicGeometry.OModulePresheaf.DevissageStep.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCover.preimage_U
AlgebraicGeometry.OModulePresheaf.sndHom_app AlgebraicGeometry.OModulePresheaf.Hom.mk.injEq
AlgebraicGeometry.OModulePresheaf.Hom.id_app
AlgebraicGeometry.OModulePresheaf.AffHom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffHom.comp_app
AlgebraicGeometry.OModulePresheaf.AffSES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.kerMap_coe
AlgebraicGeometry.OModulePresheaf.AffHom.id_app
AlgebraicGeometry.OModulePresheaf.Hom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.toAffHom_app
AlgebraicGeometry.OModulePresheaf.SES.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.AffHom.mk.sizeOf_spec
AlgebraicGeometry.OModulePresheaf.Hom.comp_app AlgebraicGeometry.OModulePresheaf.SES.mk.injEq
AlgebraicGeometry.OModulePresheaf.AffHom.mk.injEq
AlgebraicGeometry.OModulePresheaf.Hom.appSections_apply
AlgebraicGeometry.OModulePresheaf.AffSES.mk.injEq
AlgebraicGeometry.OModulePresheaf.Leray.restrictToPreimage_U
AlgebraicGeometry.Scheme.OrderedAffineCover.toCoverOf_U
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.sizeOf_spec
AlgebraicGeometry.Scheme.OrderedAffineCoverOf.mk.injEq
AlgebraicGeometry.Scheme.OrderedAffineCover.restrict_U DoubleComplex.Bounded.mk.injEq
DoubleComplex.Bounded.mk.sizeOf_spec DoubleComplex.Convergence.mk.injEq
DoubleComplex.Convergence.mk.sizeOf_spec DoubleComplex.SubQuot.mk.sizeOf_spec
DoubleComplex.SubQuot.mk.injEq AlgebraicGeometry.ChowDatumProj.mk.sizeOf_spec
attribute [-simp] AlgebraicGeometry.ChowDatum.mk.sizeOf_spec
AlgebraicGeometry.ChowDatumProj.mk.injEq AlgebraicGeometry.ChowDatum.mk.injEq
ProjSpaceCech.GradedModule.mk.injEq ProjSpaceCech.GradedModule.mk.sizeOf_spec
ProjSpaceCech.GradedModule.Frac.mk.sizeOf_spec ProjSpaceCech.GradedModule.Presentation.mk.injEq
ProjSpaceCech.GradedModule.Frac.mk.injEq ProjSpaceCech.GradedModule.Presentation.mk.sizeOf_spec
ProjSpaceCech.GradedModule.Hom.shift_toLinearMap ProjSpaceCech.GradedModule.Hom.mk.sizeOf_spec
ProjSpaceCech.GradedModule.Hom.mk.injEq AlgebraicGeometry.tilde.functorCompPullbackSpecIso_app
universe u
open CategoryTheory CategoryTheory.Limits AlgebraicGeometry TensorProduct
noncomputable section
namespace S32F2
section Transport
variable {A : Type u} [CommRing A]
{K : ℕ → Type u} [∀ i, AddCommGroup (K i)] [∀ i, Module A (K i)]
{P : ℕ → Type u} [∀ i, AddCommGroup (P i)] [∀ i, Module A (P i)]
{Q : ℕ → Type u} [∀ i, AddCommGroup (Q i)] [∀ i, Module A (Q i)]
(δ : ∀ i, K i →ₗ[A] K (i + 1)) (dP : ∀ i, P i →ₗ[A] P (i + 1)) (dQ : ∀ i, Q i →ₗ[A] Q (i + 1))
(ψ : ∀ i, K i →ₗ[A] P i) (E : ∀ i, P i ≃ₗ[A] Q i)Lean source · statement
lemma E_dP (hE : ∀ i, (E (i + 1)).toLinearMap ∘ₗ dP i = dQ i ∘ₗ (E i).toLinearMap) (i : ℕ) (x : P
i) :
E (i + 1) (dP i x) = dQ i (E i x)