diff options
Diffstat (limited to 'Data/CMonoid.agda')
| -rw-r--r-- | Data/CMonoid.agda | 25 |
1 files changed, 8 insertions, 17 deletions
diff --git a/Data/CMonoid.agda b/Data/CMonoid.agda index 8aaf869..dd0277c 100644 --- a/Data/CMonoid.agda +++ b/Data/CMonoid.agda @@ -3,19 +3,16 @@ open import Level using (Level) module Data.CMonoid {c ℓ : Level} where -open import Categories.Category.Monoidal.Bundle using (SymmetricMonoidalCategory) +import Algebra.Bundles as Alg + +open import Algebra.Morphism using (IsMonoidHomomorphism) +open import Categories.Object.Monoid using (Monoid) open import Category.Instance.Setoids.SymmetricMonoidal {c} {ℓ} using (Setoids-×; ×-symmetric′) +open import Data.Monoid {c} {ℓ} using (toMonoid; fromMonoid; toMonoid⇒; module FromMonoid) +open import Data.Product using (_,_; Σ) +open import Function using (Func; _⟨$⟩_; _⟶ₛ_) open import Object.Monoid.Commutative using (CommutativeMonoid; CommutativeMonoid⇒) -open import Categories.Object.Monoid using (Monoid) - -open import Data.Monoid {c} {ℓ} using (toMonoid; fromMonoid; toMonoid⇒) -import Algebra.Bundles as Alg - -open import Data.Setoid using (∣_∣) -open import Relation.Binary using (Setoid) -open import Function using (Func; _⟨$⟩_) -open import Data.Product using (curry′; uncurry′; _,_) open Func -- A commutative monoid object in the (symmetric monoidal) category of setoids @@ -37,9 +34,6 @@ toCMonoid M = record comm : (x y : M.Carrier) → x M.∙ y M.≈ y M.∙ x comm x y = commutative {x , y} -open import Function.Construct.Constant using () renaming (function to Const) -open import Data.Setoid.Unit using (⊤ₛ) - fromCMonoid : Alg.CommutativeMonoid c ℓ → CommutativeMonoid Setoids-×.symmetric fromCMonoid M = record { M @@ -53,7 +47,7 @@ fromCMonoid M = record module M = Monoid (fromMonoid monoid) open Setoids-× using (_≈_; _∘_; module braiding) opaque - unfolding toMonoid + unfolding FromMonoid.μ commutative : M.μ ≈ M.μ ∘ braiding.⇒.η _ commutative {x , y} = comm x y @@ -64,9 +58,6 @@ module _ (M N : CommutativeMonoid Setoids-×.symmetric) where module M = Alg.CommutativeMonoid (toCMonoid M) module N = Alg.CommutativeMonoid (toCMonoid N) - open import Data.Product using (Σ; _,_) - open import Function using (_⟶ₛ_) - open import Algebra.Morphism using (IsMonoidHomomorphism) open CommutativeMonoid open CommutativeMonoid⇒ |
