`(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))
+ `(K:PreMonoidalCat(Ob:=Ob)(bin_obj':=bobj)(I:=pmon_I(PreMonoidalCat:=C)))
(* an identity-on-objects functor J:C->Z(K) *)
:= { fc_J : Functor C (Center_is_Monoidal K) (fun x => x)