proposition: Theorem hom_fmap_counit_unit {x} : fmap[U] (hom_counit x) ∘ hom_unit (U x) ≈ id.
proof: Proof. spose (@hom_unit_naturality_consequence (U x) x (hom_counit x)) as X. rewrites. unfold hom_unit; simpl. srewrite (iso_to_from hom_adj (U x, x) id); cat. 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.Construction.Product Category.Construction.Opposite Category.Functor.Hom Category.Functor.Construction.Product Category.Functor.Opposite Category.Instance.Fun Category.Instance.Sets