major revision: MonoidalCat is now a subclass of PreMonoidalCat

[coq-categories.git] / src / FreydCategories.v

diff --git a/src/FreydCategories.v b/src/FreydCategories.v
index c50e732..3e26e37 100644 (file)
--- a/src/FreydCategories.v
+++ b/src/FreydCategories.v
@@ -14,25 +14,29 @@ Require Import Subcategories_ch7_1.
 Require Import NaturalTransformations_ch7_4.
 Require Import NaturalIsomorphisms_ch7_5.
 Require Import Coherence_ch7_8.
 Require Import NaturalTransformations_ch7_4.
 Require Import NaturalIsomorphisms_ch7_5.
 Require Import Coherence_ch7_8.

+Require Import BinoidalCategories.
+Require Import PreMonoidalCategories.
+Require Import PreMonoidalCenter.

 Require Import MonoidalCategories_ch7_8.
 
 (* A Freyd Category is... *)
 Class FreydCategory
 
   (* a cartesian category C *)
 Require Import MonoidalCategories_ch7_8.
 
 (* A Freyd Category is... *)
 Class FreydCategory
 
   (* a cartesian category C *)

-  `(C:CartesianCat(Ob:=Ob)(C:=C1)(Fobj:=fun x => bobj (fst_obj _ _ x) (snd_obj _ _ x)))
+  `(C:CartesianCat(Ob:=Ob)(C:=C1))

 
   (* 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))
 
   (* an identity-on-objects functor J:C->Z(K) *)
 
   (* 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))
 
   (* an identity-on-objects functor J:C->Z(K) *)

-:= { fc_J       : Functor C (CenterMonoidal K) (fun x => exist _ x I)
+:= { fc_J       : Functor C (Center_is_Monoidal K) (fun x => exist (fun _ => True) x I)

 
   (* which is not only monoidal *)
 
   (* which is not only monoidal *)

-   ; fc_mf_J    : MonoidalFunctor C (CenterMonoidal K) fc_J
+   ; 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, iso_forward (mf_coherence fc_mf_J a) ~~ id _
+   (* 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 *)

 
    ; fc_C       := C
    ; fc_K       := K
 
    ; fc_C       := C
    ; fc_K       := K