Require Import Subcategories_ch7_1.
Require Import NaturalTransformations_ch7_4.
Require Import NaturalIsomorphisms_ch7_5.
+Require Import BinoidalCategories.
+Require Import PreMonoidalCategories.
Require Import MonoidalCategories_ch7_8.
Require Import Coherence_ch7_8.
Require Import Enrichment_ch2_8.
: Functor s1 s2 (generalizedArrowOrIdentityFobj _ _ f) :=
match f with
| gaoi_id s => functor_id _
- | gaoi_ga s1 s2 f => ga_functor f >>>> RepresentableFunctor s2 (mon_i s2)
+ | gaoi_ga s1 s2 f => ga_functor f >>>> HomFunctor s2 (mon_i s2)
end.
Definition compose_generalizedArrows (s0 s1 s2:SMMEs) :
intro g01.
intro g12.
refine
- {| ga_functor := g01 >>>> RepresentableFunctor s1 (mon_i s1) >>>> g12 |}.
+ {| ga_functor := g01 >>>> HomFunctor s1 (mon_i s1) >>>> g12 |}.
apply MonoidalFunctorsCompose.
apply MonoidalFunctorsCompose.
apply (ga_functor_monoidal g01).