chore(library/hott): make precategory use the isomorphic structure
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1 changed files with 4 additions and 4 deletions
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@ -46,10 +46,6 @@ namespace morphism
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theorem id_is_iso [instance] : is_iso (ID a) :=
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is_iso.mk !id_compose !id_compose
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-- In a precategory, equal objects are isomorphic
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definition iso_of_path (p : a ≈ b) : Σ (f : hom a b), is_iso f :=
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path.rec_on p ⟨ id , id_is_iso ⟩
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theorem inverse_is_iso [instance] (f : a ⟶ b) [H : is_iso f] : is_iso (f⁻¹) :=
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is_iso.mk !compose_inverse !inverse_compose
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@ -150,6 +146,10 @@ namespace morphism
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--is_equivalence.mk (is_reflexive.mk refl) (is_symmetric.mk symm) (is_transitive.mk trans)
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end isomorphic
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-- In a precategory, equal objects are isomorphic
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definition iso_of_path (p : a ≈ b) : isomorphic a b :=
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path.rec_on p (isomorphic.mk id)
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inductive is_mono [class] (f : a ⟶ b) : Type :=
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mk : (∀c (g h : hom c a), f ∘ g ≈ f ∘ h → g ≈ h) → is_mono f
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inductive is_epi [class] (f : a ⟶ b) : Type :=
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