proposition: Lemma lawvere_iso_from_to {a b} (f : F a ~> b) : ψ E (φ E ((a, b); f)) ≅ ((a, b); ψ' E (φ' E f)).
proof: Proof. refine (iso_compose (lawvere_iso_from (φ' E f)) _). apply fobj_iso. now apply lawvere_iso_to. Qed.
imports: Category.Lib Category.Theory.Category Category.Theory.Isomorphism Category.Theory.Functor Category.Theory.Natural.Transformation Category.Theory.Adjunction Category.Adjunction.Natural.Transformation Category.Adjunction.Natural.Transformation.Universal Category.Construction.Comma Category.Construction.Product Category.Instance.Cat Category.Instance.Fun Category.Instance.Sets