diff --git a/src/Cat/Category/Monad.agda b/src/Cat/Category/Monad.agda index f2b6ee0..7ffe664 100644 --- a/src/Cat/Category/Monad.agda +++ b/src/Cat/Category/Monad.agda @@ -719,6 +719,19 @@ module _ {ℓa ℓb : Level} {ℂ : Category ℓa ℓb} where back : voe-2-3-2 → voe-2-3-1 back = voe-2-3-1-fromMonad ∘f Kleisli→Monoidal ∘f voe-2-3-2.toMonad + Voe-2-3-1-inverse = (toMonad ∘f fromMonad) ≡ Function.id + where + toMonad : voe-2-3-1 → M.Monad + toMonad = voe-2-3-1.toMonad + t : (m : M.Monad) → voe-2-3.voe-2-3-1 ℂ (M.Monad.Romap m) (λ {X} → M.Monad.pureT m X) + t = voe-2-3-1-fromMonad + -- Problem: `t` does not fit the type of `fromMonad`! + fromMonad : M.Monad → voe-2-3-1 + fromMonad = {!t!} + + voe-2-3-1-inverse : Voe-2-3-1-inverse + voe-2-3-1-inverse = {!!} + forthEq : ∀ m → (forth ∘f back) m ≡ m forthEq m = begin (forth ∘f back) m ≡⟨⟩