`(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:=pmon_I(PreMonoidalCat:=C)))
+ `(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 => x)
(* 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_strict_id : #(mf_i(PreMonoidalFunctor:=fc_mf_J)) ~~ id _
; fc_C := C
; fc_K := K