proposition: Proposition id_unit_left {x} : id ⨂ unit_left ≈ @unit_left _ _ (I ⨂ x).
proof: Proof. assert (unit_left ∘ id ⨂ unit_left << I ⨂ (I ⨂ x) ~~> x >> unit_left ∘ unit_left) by (rewrite to_unit_left_natural; reflexivity). symmetry. do 2 (rewrite <- id_left; symmetry). rewrite <- (iso_from_to unit_left). rewrite <- !comp_assoc. rewrites; reflexivity. Qed.
imports: Category.Lib Category.Theory.Category Category.Theory.Isomorphism Category.Theory.Functor Category.Functor.Bifunctor Category.Structure.Monoidal