import logic namespace setoid inductive setoid : Type := mk_setoid: Π (A : Type'), (A → A → Prop) → setoid set_option pp.universes true check setoid definition test : Type.{2} := setoid.{0} definition carrier (s : setoid) := setoid.rec (λ a eq, a) s definition eqv {s : setoid} : carrier s → carrier s → Prop := setoid.rec (λ a eqv, eqv) s infix `≈` := eqv coercion carrier inductive morphism (s1 s2 : setoid) : Type := mk : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism s1 s2 check morphism.mk check λ (s1 s2 : setoid), s1 check λ (s1 s2 : Type), s1 inductive morphism2 (s1 : setoid) (s2 : setoid) : Type := mk : Π (f : s1 → s2), (∀ x y, x ≈ y → f x ≈ f y) → morphism2 s1 s2 check morphism2 check morphism2.mk end setoid