--- a/limit-to.agda	Wed Dec 24 12:50:52 2014 +0900
+++ b/limit-to.agda	Wed Dec 24 22:16:20 2014 +0900
@@ -36,37 +36,30 @@
        unique-map  :  ∀{two : Two } → map← ( map two ) ≡ two
        unique-map1 :  ∀{f : Hom I (obj t0) (obj t1) } → map ( map← f ) ≡ f
 
-
 open Limit
 open TwoCat
 
+record two-Γ  {c₁ c₂ ℓ : Level} (A : Category c₁ c₂ ℓ) (I : Category c₁ c₂ ℓ) 
+       (a b : Obj A)  (f g : Hom A a b )
+       (two : Two) (twocat : TwoCat I two ) (Γ : Functor I A) : Set (suc (c₁ ⊔ c₂ ⊔ ℓ ))  where
+    field
+       a0  :  FObj Γ (obj twocat t0 ) ≡ a 
+       b0  :  FObj Γ (obj twocat t1 ) ≡ b 
+       f0  :  A [ FMap Γ (map twocat t0 ) ≈ f ]
+       g0  :  A [ FMap Γ (map twocat t0 ) ≈ g ]
+
 lim-to-equ : {c₁ c₂ ℓ : Level} (A : Category c₁ c₂ ℓ) (I : Category c₁ c₂ ℓ)
       (two : Two  ) 
       (twocat : TwoCat I two) 
+      (Γ : Functor I A)
       (lim : ( Γ : Functor I A ) → { a0 : Obj A } { u : NTrans I A ( K A I a0 ) Γ } → Limit A I Γ a0 u ) -- completeness
         →  {a b c : Obj A} (f g : Hom A a b)  → (e : Hom A c a ) → (fe=ge : A [ A [ f o e ] ≈ A [ g o e ] ] ) → Equalizer A e f g
-lim-to-equ {c₁} A I two twocat lim {a} {b} {c} f g e fe=ge = record {
+lim-to-equ {c₁} A I two twocat Γ lim {a} {b} {c} f g e fe=ge = record {
         fe=ge =  fe=ge
         ; k = λ {d} h fh=gh → k {d} h fh=gh
         ; ek=h = λ {d} {h} {fh=gh} → {!!}
         ; uniqueness = λ {d} {h} {fh=gh} {k'} → {!!}
      } where
-         Γobj :  Two {c₁} → Obj A
-         Γobj t0 = a
-         Γobj t1 = b
-         Γmap :  Two {c₁} → Hom A a b
-         Γmap t0 = f
-         Γmap t1 = g
-         Γ : Functor I A
-         Γ = record {
-            FObj  = λ x → Γobj (obj← twocat x) ;
-            FMap  = λ f → {!!} ;
-            isFunctor = record {
-                     ≈-cong  = {!!} ; 
-                    identity = {!!} ;
-                    distr = {!!}
-            }
-          }
          nat : (d : Obj A) → NTrans I A (K A I d) Γ
          nat d = record {
             TMap = λ x → {!!} ;