The repository-owned deformed slicing

The owner deformed predicate is assembled into a slicing using the sharp Hom vanishing, shift symmetry, and global HN theorem proved in the preceding modules.

def CategoryTheory.Triangulated.StabilityCondition.WithClassMap.deformedSlicing (C : Type u) [Category.{v, u} C] [Limits.HasZeroObject C] [HasShift C ℤ] [Preadditive C] [∀ (n : ℤ), (shiftFunctor C n).Additive] [Pretriangulated C] [IsTriangulated C] {Λ : Type u'} [AddCommGroup Λ] {κ : K₀ C →+ Λ} (σ : WithClassMap C κ) (W : Λ →+ ℂ) {r : ℝ} (hr0 : 0 ≤ r) (hr1 : r < 1) (hW : WeakStabilityCondition.StabilityCondition.Deformation.stabilitySeminorm C σ (W - σ.Z) ≤ ENNReal.ofReal r) {ε₀ : ℝ} (hε₀ : 0 < ε₀) (hε₀16 : ε₀ < 1 / 16) (hWide : WeakStabilityCondition.StabilityCondition.Deformation.WideSectorFiniteLength C σ ε₀) {ε : ℝ} (hε : 0 < ε) (hεhalf : ε < ε₀ / 2) (hε2 : ε ≤ 1 / 2) (hε8 : ε < 1 / 8) (hsin : WeakStabilityCondition.StabilityCondition.Deformation.stabilitySeminorm C σ (W - σ.Z) < ENNReal.ofReal (Real.sin (Real.pi * ε))) : Slicing C

The slicing defined by the repository-owned deformed phase predicate.

Equations

• One or more equations did not get rendered due to their size.

@[simp]

theorem CategoryTheory.Triangulated.StabilityCondition.WithClassMap.deformedSlicing_P (C : Type u) [Category.{v, u} C] [Limits.HasZeroObject C] [HasShift C ℤ] [Preadditive C] [∀ (n : ℤ), (shiftFunctor C n).Additive] [Pretriangulated C] [IsTriangulated C] {Λ : Type u'} [AddCommGroup Λ] {κ : K₀ C →+ Λ} (σ : WithClassMap C κ) (W : Λ →+ ℂ) {r : ℝ} (hr0 : 0 ≤ r) (hr1 : r < 1) (hW : WeakStabilityCondition.StabilityCondition.Deformation.stabilitySeminorm C σ (W - σ.Z) ≤ ENNReal.ofReal r) {ε₀ : ℝ} (hε₀ : 0 < ε₀) (hε₀16 : ε₀ < 1 / 16) (hWide : WeakStabilityCondition.StabilityCondition.Deformation.WideSectorFiniteLength C σ ε₀) {ε : ℝ} (hε : 0 < ε) (hεhalf : ε < ε₀ / 2) (hε2 : ε ≤ 1 / 2) (hε8 : ε < 1 / 8) (hsin : WeakStabilityCondition.StabilityCondition.Deformation.stabilitySeminorm C σ (W - σ.Z) < ENNReal.ofReal (Real.sin (Real.pi * ε))) (ψ : ℝ) : (deformedSlicing C σ W hr0 hr1 hW hε₀ hε₀16 hWide hε hεhalf hε2 hε8 hsin).P ψ = deformedPred C σ W hr0 hr1 hW ε ψ