fact: Definition lawvere_from_to_iso {a b} (f : F a ~> b) : ((a, b); ψ' E (φ' E f)) ≅[F ↓ Id[C]] ((a, b); f) := iso_compose (`1 (iso_from_to (lawvere_iso E)) ((a, b); f)) (iso_sym (@lawvere_iso_from_to _ _ f)).
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