Require Import MonoidalCategories_ch7_8.
Require Import Coherence_ch7_8.
Require Import Enrichment_ch2_8.
+Require Import Enrichments.
Require Import RepresentableStructure_ch7_2.
+Require Import PreMonoidalCenter.
+Require Import PreMonoidalCategories.
+Require Import BinoidalCategories.
-Class GeneralizedArrow (K:Enrichment) (C:MonoidalEnrichment) :=
-{ ga_functor_obj : enr_v_mon K -> C
-; ga_functor : Functor (enr_v_mon K) C ga_functor_obj
-; ga_functor_monoidal : MonoidalFunctor (enr_v_mon K) C ga_functor
+Class GeneralizedArrow (K:Enrichment) {ce}(C:MonoidalEnrichment ce) :=
+{ ga_functor_obj : enr_v K -> ce
+; ga_functor : Functor (enr_v_mon K) (enr_c_pm ce) ga_functor_obj
+; ga_functor_monoidal : PreMonoidalFunctor (enr_v_mon K) (enr_c_pm ce) ga_functor
+
+(* We require that the host language (but NOT the guest language) be pure, i.e. all morphisms central, to simplify
+ * things. If this doesn't suit you, just consider the "host language" here to be the pure sublanguage of the
+ * host language, and toss on the inclusion functor to the full language *)
+; ga_host_lang_pure : CommutativeCat (enr_c_pm ce)
+
+(*
+; ga_functor : Functor (enr_v_mon K) (Center_is_Monoidal (enr_c_pm ce)) ga_functor_obj
+; ga_functor_monoidal : MonoidalFunctor (enr_v_mon K) (Center_is_Monoidal (enr_c_pm ce)) ga_functor
+*)
}.
-Coercion ga_functor_monoidal : GeneralizedArrow >-> MonoidalFunctor.
+Coercion ga_functor_monoidal : GeneralizedArrow >-> PreMonoidalFunctor.
-Implicit Arguments GeneralizedArrow [ ].
-Implicit Arguments ga_functor_obj [ K C ].
-Implicit Arguments ga_functor [ K C ].
-Implicit Arguments ga_functor_monoidal [ K C ].
+Implicit Arguments GeneralizedArrow [ [ce] ].
+Implicit Arguments ga_functor_obj [ K ce C ].
+Implicit Arguments ga_functor [ K ce C ].
+Implicit Arguments ga_functor_monoidal [ K ce C ].