refactor: Lint
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1 changed files with 2 additions and 10 deletions
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@ -29,6 +29,7 @@ variable {C k : Type} [CommRing k] {G : Type} [Group G]
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namespace Discrete
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/-- Takes a homorphism in `Discrete C` to an isomorphism built on the same objects. -/
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def homToIso {c1 c2 : Discrete C} (h : c1 ⟶ c2) : c1 ≅ c2 :=
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Discrete.eqToIso (Discrete.eq_of_hom h)
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@ -38,6 +39,7 @@ namespace lift
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noncomputable section
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variable (F : Discrete C ⥤ Rep k G)
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/-- Takes a homorphisms of `Discrete C` to an isomorphism `F.obj c1 ≅ F.obj c2`. -/
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def discreteFunctorMapIso {c1 c2 : Discrete C} (h : c1 ⟶ c2) :
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F.obj c1 ≅ F.obj c2 := F.mapIso (Discrete.homToIso h)
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@ -55,7 +57,6 @@ def objObj' (f : OverColor C) : Rep k G := Rep.of {
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lemma objObj'_ρ (f : OverColor C) (M : G) : (objObj' F f).ρ M =
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PiTensorProduct.map (fun x => (F.obj (Discrete.mk (f.hom x))).ρ M) := rfl
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@[simp]
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lemma objObj'_ρ_tprod (f : OverColor C) (M : G) (x : (i : f.left) → F.obj (Discrete.mk (f.hom i))) :
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(objObj' F f).ρ M (PiTensorProduct.tprod k x) =
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PiTensorProduct.tprod k fun i => (F.obj (Discrete.mk (f.hom i))).ρ M (x i) := by
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@ -64,17 +65,8 @@ lemma objObj'_ρ_tprod (f : OverColor C) (M : G) (x : (i : f.left) → F.obj (Di
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rw [PiTensorProduct.map_tprod]
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rfl
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/-- Given a morphism in `OverColor Color` the corresopnding linear equivalence between `obj' _`
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induced by reindexing. -/
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def objMapToLinearEquiv' {f g : OverColor C} (m : f ⟶ g) :
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(objObj' F f).V ≃ₗ[k] (objObj' F g).V :=
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(PiTensorProduct.reindex k (fun x => (F.obj (Discrete.mk (f.hom x)))) (OverColor.Hom.toEquiv m)).trans
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(PiTensorProduct.congr (fun i => colorToRepCongr (OverColor.Hom.toEquiv_symm_apply m i)))
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end
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end lift
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def lift : (Discrete C ⥤ Rep k G) ⥤ (MonoidalFunctor (OverColor C) (Rep k G)) := sorry
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end OverColor
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end IndexNotation
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