almost finished with main theorem

[coq-hetmet.git] / src / GeneralizedArrowFromReification.v

diff --git a/src/GeneralizedArrowFromReification.v b/src/GeneralizedArrowFromReification.v
index 6aeaace..627aa22 100644 (file)
--- a/src/GeneralizedArrowFromReification.v
+++ b/src/GeneralizedArrowFromReification.v
@@ -26,7 +26,7 @@ Require Import GeneralizedArrow.
 
 Section GArrowFromReification.
 
-  Context  (K:SurjectiveEnrichment) (C:MonicMonoidalEnrichment) (reification : Reification K C (me_i C)).
+  Context  `(K:SurjectiveEnrichment ke) `(C:MonicMonoidalEnrichment ce cme) (reification : Reification K C (me_i C)).
 
   Fixpoint garrow_fobj_ vk : C :=
     match vk with
@@ -35,13 +35,13 @@ Section GArrowFromReification.
     | t1,,t2          => me_f C (pair_obj (garrow_fobj_ t1) (garrow_fobj_ t2))
     end.
 
-  Definition garrow_fobj vk := garrow_fobj_ (projT1 (se_decomp K vk)).
+  Definition garrow_fobj vk := garrow_fobj_ (projT1 (se_decomp _ K vk)).
 
   Definition homset_tensor_iso
     : forall vk:enr_v_mon K, (reification_rstar reification vk) ≅ ehom(ECategory:=C) (me_i C) (garrow_fobj vk).
     intros.
     unfold garrow_fobj.
-    set (se_decomp K vk) as sevk.
+    set (se_decomp _ K  vk) as sevk.
     destruct sevk.
     simpl in *.
     rewrite e.
@@ -122,9 +122,29 @@ Section GArrowFromReification.
 
   Definition garrow_functor := step1_functor >>>> step2_functor.
 
-  Definition garrow_from_reification : GeneralizedArrow K C.
-    refine {| ga_functor := garrow_functor |}.
+  Lemma garrow_functor_monoidal_niso
+    : (garrow_functor **** garrow_functor) >>>> (mon_f C) <~~~> (mon_f (enr_v_mon K)) >>>> garrow_functor.
+    admit.
+    Defined.
+  Lemma garrow_functor_monoidal_iso
+    : mon_i C ≅ garrow_functor (mon_i (enr_v_mon K)).
+    admit.
+    Defined.
+
+  Instance garrow_functor_monoidal : MonoidalFunctor (enr_v_mon K) C garrow_functor :=
+    { mf_coherence := garrow_functor_monoidal_niso
+    ; mf_id        := garrow_functor_monoidal_iso
+    }.
     admit.
+    admit.
+    admit.
+    Defined.
+
+  Definition garrow_from_reification : GeneralizedArrow K C.
+    refine
+      {| ga_functor          := garrow_functor
+       ; ga_functor_monoidal := garrow_functor_monoidal
+      |}.
     Defined.
 
 End GArrowFromReification.