Definition make_form_adjunction {A B : category} {F : functor A B} {G : functor B A} {eta : nat_trans (functor_identity A) (functor_composite F G)} {eps : nat_trans (functor_composite G F) (functor_identity B)} (H1 : ∏ a : A, # F (eta a) · eps (F a) = identity (F a)) (H2 : ∏ b : B, eta (G b) · # G (eps b) = identity (G b)) : form_adjunction F G eta eps := (H1,,H2).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.SplitMonicsAndEpis. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Section HomSetIsoRightFromPartial. End HomSetIsoRightFromPartial. Section HomSetIsoLeftFromPartial. End HomSetIsoLeftFromPartial.