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refactor: Lint

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jstoobysmith 2024-10-09 15:23:54 +00:00
parent 4054665c38
commit 05903bc440
5 changed files with 42 additions and 46 deletions
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26
HepLean/SpaceTime/WeylFermion/ColorFun.lean
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@ -172,7 +172,7 @@ lemma map_tprod {X Y : OverColor Color} (p : (i : X.left) → (colorToRep (X.hom
change (colorFun.map' f).hom ((PiTensorProduct.tprod ℂ) p) = _
simp [colorFun.map', mapToLinearEquiv']
erw [LinearEquiv.trans_apply]
change (PiTensorProduct.congr fun i => colorToRepCongr _)
change (PiTensorProduct.congr fun i => colorToRepCongr _)
((PiTensorProduct.reindex ℂ (fun x => _) (OverColor.Hom.toEquiv f))
((PiTensorProduct.tprod ℂ) p)) = _
rw [PiTensorProduct.reindex_tprod, PiTensorProduct.congr_tprod]
@ -244,8 +244,8 @@ def μModEquiv (X Y : OverColor Color) :
(colorFun.obj X ⊗ colorFun.obj Y).V ≃ₗ[ℂ] colorFun.obj (X ⊗ Y) :=
HepLean.PiTensorProduct.tmulEquiv ≪≫ₗ PiTensorProduct.congr colorToRepSumEquiv
lemma μModEquiv_tmul_tprod {X Y : OverColor Color}(p : (i : X.left) → (colorToRep (X.hom i)))
(q : (i : Y.left) → (colorToRep (Y.hom i))) :
lemma μModEquiv_tmul_tprod {X Y : OverColor Color}(p : (i : X.left) → (colorToRep (X.hom i)))
(q : (i : Y.left) → (colorToRep (Y.hom i))) :
(μModEquiv X Y) ((PiTensorProduct.tprod ℂ) p ⊗ₜ[ℂ] (PiTensorProduct.tprod ℂ) q) =
(PiTensorProduct.tprod ℂ) fun i =>
(colorToRepSumEquiv i) (HepLean.PiTensorProduct.elimPureTensor p q i) := by
@ -289,8 +289,8 @@ def μ (X Y : OverColor Color) : colorFun.obj X ⊗ colorFun.obj Y ≅ colorFun.
hom := (μModEquiv X Y).symm.toLinearMap
comm := fun M => by
simp [CategoryStruct.comp]
erw [LinearEquiv.eq_comp_toLinearMap_symm,LinearMap.comp_assoc ,
LinearEquiv.toLinearMap_symm_comp_eq ]
erw [LinearEquiv.eq_comp_toLinearMap_symm,LinearMap.comp_assoc,
LinearEquiv.toLinearMap_symm_comp_eq]
refine HepLean.PiTensorProduct.induction_tmul (fun p q => ?_)
simp only [colorFun_obj_V_carrier, OverColor.instMonoidalCategoryStruct_tensorObj_left,
OverColor.instMonoidalCategoryStruct_tensorObj_hom, Functor.id_obj, CategoryStruct.comp,
@ -325,8 +325,8 @@ def μ (X Y : OverColor Color) : colorFun.obj X ⊗ colorFun.obj Y ≅ colorFun.
LinearEquiv.symm_trans_self, LinearEquiv.refl_toLinearMap, Action.id_hom]
rfl
lemma μ_tmul_tprod {X Y : OverColor Color} (p : (i : X.left) → (colorToRep (X.hom i)))
(q : (i : Y.left) → (colorToRep (Y.hom i))) :
lemma μ_tmul_tprod {X Y : OverColor Color} (p : (i : X.left) → (colorToRep (X.hom i)))
(q : (i : Y.left) → (colorToRep (Y.hom i))) :
(μ X Y).hom.hom ((PiTensorProduct.tprod ℂ) p ⊗ₜ[ℂ] (PiTensorProduct.tprod ℂ) q) =
(PiTensorProduct.tprod ℂ) fun i =>
(colorToRepSumEquiv i) (HepLean.PiTensorProduct.elimPureTensor p q i) := by
@ -353,7 +353,7 @@ lemma μ_natural_left {X Y : OverColor Color} (f : X ⟶ Y) (Z : OverColor Color
((PiTensorProduct.tprod ℂ) p) ⊗ₜ[ℂ] ((PiTensorProduct.tprod ℂ) q)) := by rfl
erw [h1]
rw [colorFun.map_tprod]
change (μ Y Z).hom.hom (((PiTensorProduct.tprod ℂ) fun i => (colorToRepCongr _)
change (μ Y Z).hom.hom (((PiTensorProduct.tprod ℂ) fun i => (colorToRepCongr _)
(p ((OverColor.Hom.toEquiv f).symm i))) ⊗ₜ[ℂ] (PiTensorProduct.tprod ℂ) q) = _
rw [μ_tmul_tprod]
apply congrArg
@ -363,7 +363,7 @@ lemma μ_natural_left {X Y : OverColor Color} (f : X ⟶ Y) (Z : OverColor Color
| Sum.inr i => rfl
lemma μ_natural_right {X Y : OverColor Color} (X' : OverColor Color) (f : X ⟶ Y) :
MonoidalCategory.whiskerLeft (colorFun.obj X') (colorFun.map f) ≫ (μ X' Y).hom =
MonoidalCategory.whiskerLeft (colorFun.obj X') (colorFun.map f) ≫ (μ X' Y).hom =
(μ X' X).hom ≫ colorFun.map (MonoidalCategory.whiskerLeft X' f) := by
ext1
refine HepLean.PiTensorProduct.induction_tmul (fun p q => ?_)
@ -384,7 +384,7 @@ lemma μ_natural_right {X Y : OverColor Color} (X' : OverColor Color) (f : X ⟶
erw [h1]
rw [map_tprod]
change (μ X' Y).hom.hom ((PiTensorProduct.tprod ℂ) p ⊗ₜ[ℂ] (PiTensorProduct.tprod ℂ) fun i =>
(colorToRepCongr _) (q ((OverColor.Hom.toEquiv f).symm i))) = _
(colorToRepCongr _) (q ((OverColor.Hom.toEquiv f).symm i))) = _
rw [μ_tmul_tprod]
apply congrArg
funext i
@ -410,7 +410,7 @@ lemma associativity (X Y Z : OverColor Color) :
(μ X (Y ⊗ Z)).hom.hom ((((PiTensorProduct.tprod ℂ) p ⊗ₜ[ℂ] ((μ Y Z).hom.hom
((PiTensorProduct.tprod ℂ) q ⊗ₜ[ℂ] (PiTensorProduct.tprod ℂ) m)))))
rw [μ_tmul_tprod, μ_tmul_tprod]
change (colorFun.map (α_ X Y Z).hom).hom ((μ (X ⊗ Y) Z).hom.hom
change (colorFun.map (α_ X Y Z).hom).hom ((μ (X ⊗ Y) Z).hom.hom
(((PiTensorProduct.tprod ℂ) fun i => (colorToRepSumEquiv i)
(HepLean.PiTensorProduct.elimPureTensor p q i)) ⊗ₜ[ℂ] (PiTensorProduct.tprod ℂ) m)) =
(μ X (Y ⊗ Z)).hom.hom ((PiTensorProduct.tprod ℂ) p ⊗ₜ[ℂ] (PiTensorProduct.tprod ℂ) fun i =>
@ -463,7 +463,7 @@ lemma right_unitality (X : OverColor Color) : (MonoidalCategory.rightUnitor (col
OverColor.instMonoidalCategoryStruct_tensorUnit_left,
OverColor.instMonoidalCategoryStruct_tensorObj_hom, Action.instMonoidalCategory_whiskerLeft_hom,
LinearMap.coe_comp, Function.comp_apply]
change TensorProduct.rid ℂ (colorFun.obj X) ((PiTensorProduct.tprod ℂ) p ⊗ₜ[ℂ] x ) =
change TensorProduct.rid ℂ (colorFun.obj X) ((PiTensorProduct.tprod ℂ) p ⊗ₜ[ℂ] x) =
(colorFun.map (ρ_ X).hom).hom ((μ X (𝟙_ (OverColor Color))).hom.hom
((((PiTensorProduct.tprod ℂ) p ⊗ₜ[ℂ] ((PiTensorProduct.isEmptyEquiv Empty).symm x)))))
simp [PiTensorProduct.isEmptyEquiv]
@ -477,7 +477,7 @@ lemma right_unitality (X : OverColor Color) : (MonoidalCategory.rightUnitor (col
end colorFun
/-- The monoidal functor between `OverColor Color` and `Rep ℂ SL(2, ℂ)` taking a map of colors
/-- The monoidal functor between `OverColor Color` and `Rep ℂ SL(2, ℂ)` taking a map of colors
to the corresponding tensor product representation. -/
def colorFunMon : MonoidalFunctor (OverColor Color) (Rep ℂ SL(2, ℂ)) where
toFunctor := colorFun