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chore: Add doc strings

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jstoobysmith 2024-10-19 10:07:03 +00:00
parent 1f3ba14462
commit 48bec8c891
6 changed files with 27 additions and 0 deletions
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2
HepLean/Tensors/OverColor/Discrete.lean
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@ -48,6 +48,8 @@ def pairIso (c : C) : (pair F).obj (Discrete.mk c) ≅ (lift.obj F).obj (OverCol
fin_cases x
rfl
/-- The isomorphism between `F.obj (Discrete.mk c1) ⊗ F.obj (Discrete.mk c2)` and
`(lift.obj F).obj (OverColor.mk ![c1,c2])` fored by the tensorate. -/
def pairIsoSep {c1 c2 : C} : F.obj (Discrete.mk c1) ⊗ F.obj (Discrete.mk c2) ≅
(lift.obj F).obj (OverColor.mk ![c1,c2]) := by
symm

11
HepLean/Tensors/OverColor/Iso.lean
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@ -27,6 +27,8 @@ open HepLean.Fin
def equivToIso {c : X → C} (e : X ≃ Y) : mk c ≅ mk (c ∘ e.symm) :=
Hom.toIso (Over.isoMk e.toIso ((Iso.eq_inv_comp e.toIso).mp rfl))
/-- The homomorphism between `c : X → C` and `c ∘ e.symm` as objects in `OverColor C` for an
equivalence `e`. -/
def equivToHom {c : X → C} (e : X ≃ Y) : mk c ⟶ mk (c ∘ e.symm) :=
(equivToIso e).hom
@ -47,12 +49,15 @@ lemma mkSum_homToEquiv {c : X ⊕ Y → C}:
lemma mkSum_inv_homToEquiv {c : X ⊕ Y → C}:
Hom.toEquiv (mkSum c).inv = (Equiv.refl _) := by
rfl
/-- The isomorphism between objects in `OverColor C` given equality of maps. -/
def mkIso {c1 c2 : X → C} (h : c1 = c2) : mk c1 ≅ mk c2 :=
Hom.toIso (Over.isoMk (Equiv.refl _).toIso (by
subst h
rfl))
/-- The homorophism from `mk c` to `mk c1` obtaied by an equivalence and
an equality lemma. -/
def equivToHomEq {c : X → C} {c1 : Y → C} (e : X ≃ Y)
(h : ∀ x, c1 x = (c ∘ e.symm) x := by decide) : mk c ⟶ mk c1 :=
(equivToHom e).trans (mkIso (funext fun x => (h x).symm)).hom
@ -71,6 +76,7 @@ def fin2Iso {c : Fin 2 → C} : mk c ≅ mk ![c 0] ⊗ mk ![c 1] := by
fin_cases x
rfl
/-- Removes a given `i : Fin n.succ.succ` from a morphism in `OverColor C`. -/
def extractOne {n : ℕ} (i : Fin n.succ.succ)
{c1 c2 : Fin n.succ.succ → C} (σ : mk c1 ⟶ mk c2) :
mk (c1 ∘ Fin.succAbove ((Hom.toEquiv σ).symm i)) ⟶ mk (c2 ∘ Fin.succAbove i) :=
@ -96,6 +102,7 @@ lemma extractOne_homToEquiv {n : ℕ} (i : Fin n.succ.succ)
(finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)) := by
rfl
/-- Removes a given `i : Fin n.succ.succ` and `j : Fin n.succ` from a morphism in `OverColor C`. -/
def extractTwo {n : ℕ} (i : Fin n.succ.succ) (j : Fin n.succ)
{c1 c2 : Fin n.succ.succ → C} (σ : mk c1 ⟶ mk c2) :
mk (c1 ∘ Fin.succAbove ((Hom.toEquiv σ).symm i) ∘
@ -107,6 +114,8 @@ def extractTwo {n : ℕ} (i : Fin n.succ.succ) (j : Fin n.succ)
equivToHomEq (Equiv.refl _) (by simp) ≫ extractOne j (extractOne i σ) ≫
equivToHomEq (Equiv.refl _) (by simp)
/-- Removes a given `i : Fin n.succ.succ` and `j : Fin n.succ` from a morphism in `OverColor C`.
This is from and to different (by equivalent) objects to `extractTwo`. -/
def extractTwoAux {n : ℕ} (i : Fin n.succ.succ) (j : Fin n.succ)
{c c1 : Fin n.succ.succ → C} (σ : mk c ⟶ mk c1) :
mk ((c ∘ ⇑(finExtractTwo ((Hom.toEquiv σ).symm i)
@ -114,6 +123,8 @@ def extractTwoAux {n : ℕ} (i : Fin n.succ.succ) (j : Fin n.succ)
mk ((c1 ∘ ⇑(finExtractTwo i j).symm) ∘ Sum.inr) :=
equivToHomEq (Equiv.refl _) (by simp) ≫ extractTwo i j σ ≫ equivToHomEq (Equiv.refl _) (by simp)
/-- Given a morphism ` mk c ⟶ mk c1` the corresponding morphism on the `Fin 1 ⊕ Fin 1` maps
obtained by extracting `i` and `j`. -/
def extractTwoAux' {n : ℕ} (i : Fin n.succ.succ) (j : Fin n.succ)
{c c1 : Fin n.succ.succ → C} (σ : mk c ⟶ mk c1) :
mk ((c ∘ ⇑(finExtractTwo ((Hom.toEquiv σ).symm i)