`{Funext} {σ} {A B : object (precategory_algebra σ)} : A ≅ B → A <~=~> B. Proof. intros [f F G]. set (h := BuildHomomorphism f). apply (@Morphisms.Build_Isomorphic _ A B h). apply (@Morphisms.Build_IsIsomorphism _ A B h (hom_inv h)). - apply path_hset_homomorphism. funext s x. apply eissect. - apply path_hset_homomorphism. funext s x. apply eisretr. Defined.
Require Import Import Morphisms.CategoryMorphismsNotations isomorphic_notations.