feat(hott): remove multiple_instances attribute
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4 changed files with 3 additions and 7 deletions
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@ -34,8 +34,6 @@ namespace category
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-- without it, we would have to explicitly use category.to_precategory
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attribute category.to_precategory [coercion]
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attribute category [multiple_instances]
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abbreviation iso_of_path_equiv := @category.iso_of_path_equiv
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attribute category.iso_of_path_equiv [instance]
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@ -54,8 +54,8 @@ namespace category
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end
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theorem reflect_inverse (F : C ⇒ D) [H : fully_faithful F] {c c' : C} (f : c ⟶ c')
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[H : is_iso f] : (to_fun_hom F)⁻¹ᶠ (F f)⁻¹ = f⁻¹ :=
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inverse_eq_inverse (idp : to_hom (@(iso.mk f) (reflect_is_iso F f)) = f)
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[H' : is_iso f] : (to_fun_hom F)⁻¹ᶠ (F f)⁻¹ = f⁻¹ :=
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@inverse_eq_inverse _ _ _ _ _ _ (reflect_is_iso F f) H' idp
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definition hom_equiv_F_hom_F [constructor] (F : C ⇒ D)
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[H : fully_faithful F] (c c' : C) : (c ⟶ c') ≃ (F c ⟶ F c') :=
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@ -22,7 +22,6 @@ namespace iso
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attribute is_iso.inverse [reducible]
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attribute is_iso [multiple_instances]
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open split_mono split_epi is_iso
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abbreviation retraction_of [unfold 6] := @split_mono.retraction_of
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abbreviation retraction_comp [unfold 6] := @split_mono.retraction_comp
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@ -79,7 +78,7 @@ namespace iso
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is_iso.mk _ ((retraction_eq_section f) ▸ (retraction_comp f)) (comp_section f)
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theorem inverse_unique (H H' : is_iso f) : @inverse _ _ _ _ f H = @inverse _ _ _ _ f H' :=
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inverse_eq_left !left_inverse
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@inverse_eq_left _ _ _ _ _ _ H !left_inverse
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theorem inverse_involutive (f : a ⟶ b) [H : is_iso f] [H : is_iso (f⁻¹)]
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: (f⁻¹)⁻¹ = f :=
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@ -30,7 +30,6 @@ namespace category
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(id_id : Π (a : ob), comp !ID !ID = ID a)
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(is_set_hom : Π(a b : ob), is_set (hom a b))
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-- attribute precategory [multiple-instances] --this is not used anywhere
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attribute precategory.is_set_hom [instance]
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infixr ∘ := precategory.comp
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