X-Git-Url: http://git.megacz.com/?p=coq-categories.git;a=blobdiff_plain;f=src%2FFreydCategories.v;h=8b921dfb79f7a14d2083c9226e3f3450697d359a;hp=3e26e376592aa1157989e362e2c6884b237cd31d;hb=658181bed516646957267b055341d9d4b197ed0d;hpb=27ffdd2265eb1c15acc62970f49d25a07bcadb05

diff --git a/src/FreydCategories.v b/src/FreydCategories.v
index 3e26e37..8b921df 100644
--- a/src/FreydCategories.v
+++ b/src/FreydCategories.v
@@ -3,8 +3,7 @@
 (*******************************************************************************)
 
 Generalizable All Variables.
-Require Import Preamble.
-Require Import General.
+Require Import Notations.
 Require Import Categories_ch1_3.
 Require Import Functors_ch1_4.
 Require Import Isomorphisms_ch1_5.
@@ -22,21 +21,21 @@ Require Import MonoidalCategories_ch7_8.
 (* A Freyd Category is... *)
 Class FreydCategory
 
-  (* a cartesian category C *)
-  `(C:CartesianCat(Ob:=Ob)(C:=C1))
+   (* a cartesian category C *)
+  `(C:CartesianCat(Ob:=Ob)(C:=C1)(bin_obj':=bobj))
 
-  (* a premonoidal category K with the same objects (its unit object is 1 because the functor is both IIO and strict) *)
-  `(K:PreMonoidalCat(Ob:=Ob)(bin_obj':=bobj)(I:=@one _ _ _ C))
+   (* a premonoidal category K with the same objects (its unit object is 1 because the functor is both IIO and strict) *)
+  `(K:PreMonoidalCat(Ob:=Ob)(bin_obj':=bobj)(I:=pmon_I C))
 
-  (* an identity-on-objects functor J:C->Z(K) *)
-:= { fc_J       : Functor C (Center_is_Monoidal K) (fun x => exist (fun _ => True) x I)
+   (* an identity-on-objects functor J:C->Z(K) *)
+:= { fc_J       : Functor C (Center_is_Monoidal K) (fun x => x)
 
-  (* which is not only monoidal *)
+   (* which is a monoidal functor *)
    ; fc_mf_J    : MonoidalFunctor C (Center_is_Monoidal K) fc_J
 
-   (* but in fact strict (meaning the functor's coherence maps are identities) *)
-   (*; fc_strict  : forall a b, #(mf_first a b) ~~ id _ 
-         FIXME - I will need to separate Subcategory from FullSubCategory in order to fix this *)
+   (* and strict (meaning the functor's coherence maps are identities) *)
+   ; fc_strict_first   : forall a b, #(mf_first(PreMonoidalFunctor:=fc_mf_J) a b) ~~ id _  (* mf_consistent gives us mf_second *)
+   ; fc_strict_id      : #(mf_i(PreMonoidalFunctor:=fc_mf_J)) ~~ id _
 
    ; fc_C       := C
    ; fc_K       := K