diff --git a/src/Cat/Category/Monad/Voevodsky.agda b/src/Cat/Category/Monad/Voevodsky.agda index f30aa9a..dfcdbda 100644 --- a/src/Cat/Category/Monad/Voevodsky.agda +++ b/src/Cat/Category/Monad/Voevodsky.agda @@ -72,12 +72,12 @@ module voe {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where } field - isMnd : IsMonad rawMnd + isMonad : IsMonad rawMnd toMonad : Monad toMonad = record { raw = rawMnd - ; isMonad = isMnd + ; isMonad = isMonad } record §2 : Set ℓ where @@ -94,36 +94,30 @@ module voe {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where } field - isMnd : IsMonad rawMnd + isMonad : IsMonad rawMnd toMonad : Monad toMonad = record { raw = rawMnd - ; isMonad = isMnd + ; isMonad = isMonad } §1-fromMonad : (m : M.Monad) → §2-3.§1 (M.Monad.Romap m) (λ {X} → M.Monad.pureT m X) - -- voe-2-3-1-fromMonad : (m : M.Monad) → voe.§2-3.§1 (M.Monad.Romap m) (λ {X} → M.Monad.pureT m X) §1-fromMonad m = record - { fmap = Functor.fmap R + { fmap = Functor.fmap R ; RisFunctor = Functor.isFunctor R - ; pureN = pureN - ; join = λ {X} → joinT X - ; joinN = joinN - ; isMnd = M.Monad.isMonad m + ; pureN = pureN + ; join = λ {X} → joinT X + ; joinN = joinN + ; isMonad = M.Monad.isMonad m } where - raw = M.Monad.raw m - R = M.RawMonad.R raw - pureT = M.RawMonad.pureT raw - pureN = M.RawMonad.pureN raw - joinT = M.RawMonad.joinT raw - joinN = M.RawMonad.joinN raw + open M.Monad m §2-fromMonad : (m : K.Monad) → §2-3.§2 (K.Monad.omap m) (K.Monad.pure m) §2-fromMonad m = record - { bind = K.Monad.bind m - ; isMnd = K.Monad.isMonad m + { bind = K.Monad.bind m + ; isMonad = K.Monad.isMonad m } -- | In the following we seek to transform the equivalence `Monoidal≃Kleisli`