Proposition lax_extension_companion_conjoint {V : quantale_cosmos} {F : SET ⟶ SET} (L : lax_extension V F) {W X Y Z : hSet} (f : W → X) (g : Z → Y) (R : enriched_relation V X Y) : L _ _ (f^* ·e R ·e g^o) = (#F f)^* ·e L _ _ R ·e (#F g)^o. Proof. rewrite <- lax_extension_companion_left. rewrite lax_extension_conjoint_right. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichedRelation. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.Limits.Coproducts. Import MonoidalNotations.