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fix(group_theory): make group_fun an abbreviation

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this fixes an error where the elaborator wouldn't unify `group_fun (homomorphism_compose g f) x` with `ap (group_fun g) ?M`
This commit is contained in:
Floris van Doorn 2017-06-14 18:41:35 -04:00
parent 7d0eecc449
commit 8a7319244f
1 changed files with 5 additions and 5 deletions
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10
hott/algebra/group_theory.hlean
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@ -46,7 +46,7 @@ namespace group
infix ` →g `:55 := homomorphism infix ` →g `:55 := homomorphism
definition group_fun [unfold 3] [coercion] := @homomorphism.φ abbreviation group_fun [unfold 3] [coercion] [reducible] := @homomorphism.φ
definition homomorphism.struct [unfold 3] [instance] [priority 900] {G₁ G₂ : Group} definition homomorphism.struct [unfold 3] [instance] [priority 900] {G₁ G₂ : Group}
(φ : G₁ →g G₂) : is_mul_hom φ := (φ : G₁ →g G₂) : is_mul_hom φ :=
homomorphism.p φ homomorphism.p φ
@ -96,7 +96,7 @@ namespace group
homomorphism.mk f homomorphism.mk f
(λg h, (p (g * h))⁻¹ ⬝ to_respect_mul φ g h ⬝ ap011 mul (p g) (p h)) (λg h, (p (g * h))⁻¹ ⬝ to_respect_mul φ g h ⬝ ap011 mul (p g) (p h))
definition homomorphism_eq (p : group_fun φ₁ ~ group_fun φ₂) : φ₁ = φ₂ := definition homomorphism_eq (p : φ₁ ~ φ₂) : φ₁ = φ₂ :=
begin begin
induction φ₁ with φ₁ q₁, induction φ₂ with φ₂ q₂, esimp at p, induction p, induction φ₁ with φ₁ q₁, induction φ₂ with φ₂ q₂, esimp at p, induction p,
exact ap (homomorphism.mk φ₁) !is_prop.elim exact ap (homomorphism.mk φ₁) !is_prop.elim
@ -143,7 +143,7 @@ namespace group
/- categorical structure of groups + homomorphisms -/ /- categorical structure of groups + homomorphisms -/
definition homomorphism_compose [constructor] [trans] (ψ : G₂ →g G₃) (φ : G₁ →g G₂) : G₁ →g G₃ := definition homomorphism_compose [constructor] [trans] [reducible] (ψ : G₂ →g G₃) (φ : G₁ →g G₂) : G₁ →g G₃ :=
homomorphism.mk (ψ ∘ φ) (is_mul_hom_compose _ _) homomorphism.mk (ψ ∘ φ) (is_mul_hom_compose _ _)
variable (G) variable (G)
@ -230,7 +230,7 @@ namespace group
definition add_homomorphism (G H : AddGroup) : Type := homomorphism G H definition add_homomorphism (G H : AddGroup) : Type := homomorphism G H
infix ` →a `:55 := add_homomorphism infix ` →a `:55 := add_homomorphism
definition agroup_fun [coercion] [unfold 3] [reducible] {G H : AddGroup} (φ : G →a H) : G → H := abbreviation agroup_fun [coercion] [unfold 3] [reducible] {G H : AddGroup} (φ : G →a H) : G → H :=
φ φ
definition add_homomorphism.struct [instance] {G H : AddGroup} (φ : G →a H) : is_add_hom φ := definition add_homomorphism.struct [instance] {G H : AddGroup} (φ : G →a H) : is_add_hom φ :=
@ -239,7 +239,7 @@ namespace group
definition add_homomorphism.mk [constructor] {G H : AddGroup} (φ : G → H) (h : is_add_hom φ) : G →g H := definition add_homomorphism.mk [constructor] {G H : AddGroup} (φ : G → H) (h : is_add_hom φ) : G →g H :=
homomorphism.mk φ h homomorphism.mk φ h
definition add_homomorphism_compose [constructor] [trans] {G₁ G₂ G₃ : AddGroup} definition add_homomorphism_compose [constructor] [trans] [reducible] {G₁ G₂ G₃ : AddGroup}
(ψ : G₂ →a G₃) (φ : G₁ →a G₂) : G₁ →a G₃ := (ψ : G₂ →a G₃) (φ : G₁ →a G₂) : G₁ →a G₃ :=
add_homomorphism.mk (ψ ∘ φ) (is_add_hom_compose _ _) add_homomorphism.mk (ψ ∘ φ) (is_add_hom_compose _ _)