Mercurial > hg > Members > kono > Proof > category
diff CCC.agda @ 793:f37f11e1b871
Hom a,b = Hom 1 b^a
author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Mon, 22 Apr 2019 02:41:53 +0900 |
parents | 4e1e2f7199c8 |
children | ba575c73ea48 |
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--- a/CCC.agda Sun Apr 21 18:11:14 2019 +0900 +++ b/CCC.agda Mon Apr 22 02:41:53 2019 +0900 @@ -22,7 +22,7 @@ : Set ( c₁ ⊔ c₂ ⊔ ℓ ) where field -- cartesian - e2 : {a : Obj A} → ∀ ( f : Hom A a 1 ) → A [ f ≈ ○ a ] + e2 : {a : Obj A} → ∀ { f : Hom A a 1 } → A [ f ≈ ○ a ] e3a : {a b c : Obj A} → { f : Hom A c a }{ g : Hom A c b } → A [ A [ π o < f , g > ] ≈ f ] e3b : {a b c : Obj A} → { f : Hom A c a }{ g : Hom A c b } → A [ A [ π' o < f , g > ] ≈ g ] e3c : {a b c : Obj A} → { h : Hom A c (a ∧ b) } → A [ < A [ π o h ] , A [ π' o h ] > ≈ h ] @@ -35,13 +35,13 @@ e'2 : A [ ○ 1 ≈ id1 A 1 ] e'2 = let open ≈-Reasoning A in begin ○ 1 - ≈↑⟨ e2 (id1 A 1 ) ⟩ + ≈↑⟨ e2 ⟩ id1 A 1 ∎ e''2 : {a b : Obj A} {f : Hom A a b } → A [ A [ ○ b o f ] ≈ ○ a ] e''2 {a} {b} {f} = let open ≈-Reasoning A in begin ○ b o f - ≈⟨ e2 (○ b o f) ⟩ + ≈⟨ e2 ⟩ ○ a ∎ π-id : {a b : Obj A} → A [ < π , π' > ≈ id1 A (a ∧ b ) ]