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changeset 210:51c57efe89b9

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α b1
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Mon, 02 Sep 2013 22:21:51 +0900
parents 4e138cc953f3
children 8c738327df19
files equalizer.agda
diffstat 1 files changed, 16 insertions(+), 16 deletions(-) [+]
line wrap: on
line diff
--- a/equalizer.agda	Mon Sep 02 21:59:37 2013 +0900
+++ b/equalizer.agda	Mon Sep 02 22:21:51 2013 +0900
@@ -34,28 +34,28 @@
 
 record EqEqualizer { c₁ c₂ ℓ : Level} ( A : Category c₁ c₂ ℓ )  {c a b : Obj A} (f g : Hom A a b) : Set  (ℓ ⊔ (c₁ ⊔ c₂)) where
    field
-      α : {e a : Obj A } → (f : Hom A a b) → (g : Hom A a b ) →  Hom A e a
-      γ : {d e a b : Obj A}  → (f : Hom A a b) → (g : Hom A a b ) → (h : Hom A d a ) →  Hom A c e 
-      δ : {a b : Obj A}  → (f : Hom A a b) → Hom A a c 
-      b1 : {e : Obj A } →  A [ A [ f  o α {e} {a} f g ] ≈ A [ g  o α {e} {a} f g ] ]
-      b2 :  {e d : Obj A } → {h : Hom A d a } → A [ A [ α {e} f g o γ f g h ] ≈ A [ h  o α {c} (A [ f o h ]) (A [ g o h ]) ] ]
-      b3 :  {e : Obj A} → A [ A [ α f f o δ f ] ≈ id1 A a ]
+      α : (f : Hom A a b) → (g : Hom A a b ) →  Hom A c a
+--      γ : {d e a b : Obj A}  → (f : Hom A a b) → (g : Hom A a b ) → (h : Hom A d a ) →  Hom A c e 
+--      δ : {a b : Obj A}  → (f : Hom A a b) → Hom A a c 
+      b1 : {e : Obj A } →  A [ A [ f  o α  f g ] ≈ A [ g  o α f g ] ]
+--      b2 :  {e d : Obj A } → {h : Hom A d a } → A [ A [ α {e} f g o γ f g h ] ≈ A [ h  o α {c} (A [ f o h ]) (A [ g o h ]) ] ]
+--      b3 :  {e : Obj A} → A [ A [ α f f o δ f ] ≈ id1 A a ]
       -- b4 :  {c d : Obj A } {k : Hom A c a} → A [ β f g ( A [ α f g o  k ] ) ≈ k ]
-      b4 :  {d : Obj A } {k : Hom A d c} → A [ A [ γ f g ( A [ α f g o  k ] ) o δ (A [ f o A [ α f g o  k ] ] ) ] ≈ k ]
+--      b4 :  {d : Obj A } {k : Hom A d c} → A [ A [ γ f g ( A [ α f g o  k ] ) o δ (A [ f o A [ α f g o  k ] ] ) ] ≈ k ]
    --  A [ α f g o β f g h ] ≈ h
-   β : { d e a b : Obj A}  → (f : Hom A a b) → (g : Hom A a b ) →  (h : Hom A d a ) → Hom A d e
-   β {d} f g h =  A [ γ f g h o δ {d} (A [ f o h ]) ] 
+--   β : { d e a b : Obj A}  → (f : Hom A a b) → (g : Hom A a b ) →  (h : Hom A d a ) → Hom A d e
+--   β {d} f g h =  A [ γ f g h o δ {d} (A [ f o h ]) ] 
 
 open Equalizer
 open EqEqualizer
 
 lemma-equ1 :  { c₁ c₂ ℓ : Level} ( A : Category c₁ c₂ ℓ )  {a b c : Obj A} (f g : Hom A a b)  → Equalizer A {c} f g → EqEqualizer A {c} f g
 lemma-equ1  A {a} {b} {c} f g eqa = record {
-      α = λ {e'} {a} f g →  ? ; -- e' -> c  c -> a,  Hom A e' a
-      γ = λ {d} {e} {a} {b} f g h → {!!} ;  -- Hom A c e
-      δ =  λ {a} {b} f → {!!} ; -- Hom A a c
-      b1 = {!!} ;
-      b2 = {!!} ;
-      b3 = {!!} ;
-      b4 = {!!} 
+      α = λ f g →  e eqa ; -- Hom A c  a
+--      γ = λ {d} {e} {a} {b} f g h → {!!} ;  -- Hom A c e
+--      δ =  λ {a} {b} f → {!!} ; -- Hom A a c
+      b1 = ef=eg eqa -- ;
+--      b2 = {!!} ;
+--      b3 = {!!} ;
+--      b4 = {!!} 
  }