- Section ArrowInLanguage.
- Context {MF}{mn:MonoidalCat TypesL (fun x => (fst_obj _ _ x),,(snd_obj _ _ x)) MF []} (CC:CartesianCat mn).
- Context {Kehom}(K:@ECategory _ _ TypesL _ mn [] mn TypesL Kehom).
- Context {bc:BinoidalCat (Underlying K) (@T_Branch _)}.
- Context (pmc:@PreMonoidalCat _ _ _ _ bc (@one _ _ _ (car_terminal(CartesianCat:=CC)))).
- Definition ArrowInProgrammingLanguage := @FreydCategory _ _ _ _ _ _ mn _ _ _ _ pmc.
- End ArrowInLanguage.
+ (* an Arrow In A Programming Language consists of... *)
+
+ (* a host language: *)
+ Context `(Host:ProgrammingLanguage).
+
+ (* ... for which Types(L) is cartesian: *)
+ Context {MF}(center_of_TypesL:MonoidalCat (TypesL _ _ Host) (fun x => (fst_obj _ _ x),,(snd_obj _ _ x)) MF []).
+
+ (* along with a monoidal subcategory of Z(Types(L)) *)
+ Context (VK:MonoidalSubCat center_of_TypesL).