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Prove propositionality for IsMonad

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Frederik Hanghøj Iversen 2018-03-02 13:31:46 +01:00
parent c4e3625746
commit b079f5e426
2 changed files with 11 additions and 6 deletions
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2
src/Cat/Category.agda
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@ -194,7 +194,7 @@ record IsCategory {ℓa ℓb : Level} (ℂ : RawCategory ℓa ℓb) : Set (lsuc
-- --
-- Proves that all projections of `IsCategory` are mere propositions as well as -- Proves that all projections of `IsCategory` are mere propositions as well as
-- `IsCategory` itself being a mere proposition. -- `IsCategory` itself being a mere proposition.
module _ {ℓa ℓb : Level} {C : RawCategory ℓa ℓb} where module Propositionality {ℓa ℓb : Level} {C : RawCategory ℓa ℓb} where
open RawCategory C open RawCategory C
module _ (ℂ : IsCategory C) where module _ (ℂ : IsCategory C) where
open IsCategory ℂ using (isAssociative ; arrowsAreSets ; isIdentity ; Univalent) open IsCategory ℂ using (isAssociative ; arrowsAreSets ; isIdentity ; Univalent)

15
src/Cat/Category/Monad.agda
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@ -8,7 +8,7 @@ open import Data.Product
open import Cubical open import Cubical
open import Cubical.NType.Properties using (lemPropF) open import Cubical.NType.Properties using (lemPropF)
open import Cat.Category hiding (propIsAssociative ; propIsIdentity) open import Cat.Category
open import Cat.Category.Functor as F open import Cat.Category.Functor as F
open import Cat.Category.NaturalTransformation open import Cat.Category.NaturalTransformation
open import Cat.Categories.Fun open import Cat.Categories.Fun
@ -375,10 +375,15 @@ module Kleisli {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
module _ (raw : RawMonad) where module _ (raw : RawMonad) where
open RawMonad raw open RawMonad raw
postulate propIsIdentity : isProp IsIdentity
propIsIdentity : isProp IsIdentity propIsIdentity x y i = ℂ.arrowsAreSets _ _ x y i
propIsNatural : isProp IsNatural propIsNatural : isProp IsNatural
propIsDistributive : isProp IsDistributive propIsNatural x y i = λ f
→ ℂ.arrowsAreSets _ _ (x f) (y f) i
propIsDistributive : isProp IsDistributive
propIsDistributive x y i = λ g f
→ ℂ.arrowsAreSets _ _ (x g f) (y g f) i
open IsMonad open IsMonad
propIsMonad : (raw : _) → isProp (IsMonad raw) propIsMonad : (raw : _) → isProp (IsMonad raw)
IsMonad.isIdentity (propIsMonad raw x y i) IsMonad.isIdentity (propIsMonad raw x y i)