--- a/comparison-em.agda	Thu Aug 01 18:14:42 2013 +0900
+++ b/comparison-em.agda	Fri Aug 02 08:21:32 2013 +0900
@@ -24,9 +24,9 @@
       { U^K : Functor B A } { F^K : Functor A B }
       { η^K : NTrans A A identityFunctor ( U^K ○ F^K ) }
       { ε^K : NTrans B B ( F^K ○ U^K ) identityFunctor } 
-      { μ^K' : NTrans A A (( U^K ○ F^K ) ○ ( U^K ○ F^K )) ( U^K ○ F^K ) }
+      { μ^K : NTrans A A (( U^K ○ F^K ) ○ ( U^K ○ F^K )) ( U^K ○ F^K ) }
       ( Adj^K : Adjunction A B U^K F^K η^K ε^K )
-      ( RK : MResolution A B T U^K F^K {η^K} {ε^K} {μ^K'} AdjK )
+      ( RK : MResolution A B T U^K F^K {η^K} {ε^K} {μ^K} Adj^K )
 where
 
 open import adj-monad
@@ -36,17 +36,13 @@
 M : Monad A (U^K ○ F^K ) η^K μ^K 
 M =  Adj2Monad A B {U^K} {F^K} {η^K} {ε^K} Adj^K
 
-K : Eilenberg-MooreCategory A (U^K ○ F^K ) η^K μ^K M 
-K = record {}
-
-open import nat {c₁} {c₂} {ℓ} {A} { U^K ○ F^K } { η^K } { μ^K } { M } { K }
+open import em-category {c₁} {c₂} {ℓ} {A} { U^K ○ F^K } { η^K } { μ^K } { M } 
 
 open Functor
 open NTrans
-open Eilenberg-MooreCategory
-open EMHom
 open Adjunction
 open MResolution
+open Eilenberg-Moore-Hom
 
 emkobj : Obj B -> EMObj
 emkobj b = record { 
@@ -58,7 +54,7 @@
       eval1 = ?
 
 emkmap : {a b : Obj B} (f : Hom B a b) -> EMHom (emkobj a) (emkobj b)
-emkmap {a} {b} f = record { EMap = FMap U f ; homomorphism = homomorphism1 
+emkmap {a} {b} f = record { EMap = FMap U^K f ; homomorphism = homomorphism1 
   } where
       homomorphism1 : ?
       homomorphism1 = ?
@@ -73,24 +69,24 @@
              ; distr    = distr1
         }
      }  where
-         identity : {a : Obj A} →  B [ emkmap (K-id {a}) ≈ id1 B (FObj F^K a) ]
+         identity : {a : Obj A} →  B [ emkmap (EM-id {a}) ≈ id1 B (FObj F^K a) ]
          identity {a} = let open ≈-Reasoning (B) in
            begin
-               emkmap (K-id {a})
+               emkmap (EM-id {a})
            ≈⟨ ? ⟩
               id1 B (FObj F^K a)
            ∎
-         ≈-cong : {a b : Obj A} -> {f g : EMHom a b} → A [ KMap f ≈ KMap g ] → B [ emkmap f ≈ emkmap g ]
+         ≈-cong : {a b : Obj A} -> {f g : EMHom a b} → A [ EMap f ≈ EMap g ] → B [ emkmap f ≈ emkmap g ]
          ≈-cong {a} {b} {f} {g} f≈g = let open ≈-Reasoning (B) in
            begin
                emkmap f
            ≈⟨ ? ⟩
                emkmap g
            ∎
-         distr1 :  {a b c : Obj A} {f : EMHom a b} {g : EMHom b c} → B [ emkmap (g * f) ≈ (B [ emkmap g o emkmap f ] )]
+         distr1 :  {a b c : Obj A} {f : EMHom a b} {g : EMHom b c} → B [ emkmap (g ∙ f) ≈ (B [ emkmap g o emkmap f ] )]
          distr1 {a} {b} {c} {f} {g} = let open ≈-Reasoning (B) in
            begin
-              emkmap (g * f)
+              emkmap (g ∙ f)
            ≈⟨ ? ⟩
               emkmap g o emkmap f
            ∎