Homomorphism A A := BuildHomomorphism (λ s x, x). End . Section hom_inv. Context {σ} {A B : Algebra σ} (f : ∀ s, A s → B s) `{IsIsomorphism σ A B f}. Global Instance is_homomorphism_inv : IsHomomorphism (λ s, (f s)^-1). Proof. intro u. generalize u.#A u.#B (oppreserving_hom f u). intros a b P. induction (σ u). - destruct P. apply (eissect (f t)). - intro. apply IHs. exact (transport (λ y, OpPreserving f _ (b y)) (eisretr (f t) x) (P (_^-1 x))). Defined.
Require Import Import algebra_notations ne_list.notations.