Library HoTT.Categories.Profunctor.Identity
Require Import Category.Core Profunctor.Core HomFunctor.
Set Universe Polymorphism.
Set Implicit Arguments.
Generalizable All Variables.
Set Asymmetric Patterns.
Local Open Scope profunctor_scope.
Section identity.
Set Universe Polymorphism.
Set Implicit Arguments.
Generalizable All Variables.
Set Asymmetric Patterns.
Local Open Scope profunctor_scope.
Section identity.
Quoting nCatLab:
In particular the identity profunctor Id : C ⇸ C is represented by the identity functor and hence is given by the hom-functor C(−,−) : Cᵒᵖ × C → Set.
Definition identity `{Funext} (C : PreCategory) : C -|-> C
:= hom_functor C.
End identity.
Module Export ProfunctorIdentityNotations.
Notation "1" := (identity _) : profunctor_scope.
End ProfunctorIdentityNotations.