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Diffstat (limited to 'Functor/Free/Instance/SymmetricMonoidalPreorder.agda')
| -rw-r--r-- | Functor/Free/Instance/SymmetricMonoidalPreorder.agda | 67 |
1 files changed, 0 insertions, 67 deletions
diff --git a/Functor/Free/Instance/SymmetricMonoidalPreorder.agda b/Functor/Free/Instance/SymmetricMonoidalPreorder.agda deleted file mode 100644 index 2fcecce..0000000 --- a/Functor/Free/Instance/SymmetricMonoidalPreorder.agda +++ /dev/null @@ -1,67 +0,0 @@ -{-# OPTIONS --without-K --safe #-} - -module Functor.Free.Instance.SymmetricMonoidalPreorder where - -import Functor.Free.Instance.MonoidalPreorder as MP - -open import Categories.Category using (Category) -open import Category.Instance.SymMonCat using (SymMonCat) -open import Categories.Category.Monoidal.Bundle using (SymmetricMonoidalCategory) -open import Categories.Functor using (Functor) -open import Categories.Functor.Monoidal.Symmetric using () renaming (module Lax to Lax₁) -open import Categories.Functor.Monoidal.Symmetric.Properties using (∘-SymmetricMonoidal) -open import Categories.NaturalTransformation.NaturalIsomorphism.Monoidal.Symmetric using () renaming (module Lax to Lax₂) -open import Category.Instance.SymMonPre.Primitive using (SymMonPre; _≃_; module ≃) -open import Data.Product using (_,_) -open import Level using (Level) -open import Preorder.Primitive.Monoidal using (MonoidalPreorder; SymmetricMonoidalPreorder; SymmetricMonoidalMonotone) - -open Lax₁ using (SymmetricMonoidalFunctor) -open Lax₂ using (SymmetricMonoidalNaturalIsomorphism) - --- The free symmetric monoidal preorder of a symmetric monoidal category - -module _ {o ℓ e : Level} where - - symmetricMonoidalPreorder : SymmetricMonoidalCategory o ℓ e → SymmetricMonoidalPreorder o ℓ - symmetricMonoidalPreorder C = record - { M - ; symmetric = record - { symmetric = λ x y → braiding.⇒.η (x , y) - } - } - where - open SymmetricMonoidalCategory C - module M = MonoidalPreorder (MP.Free.₀ monoidalCategory) - - module _ {A B : SymmetricMonoidalCategory o ℓ e} where - - symmetricMonoidalMonotone - : SymmetricMonoidalFunctor A B - → SymmetricMonoidalMonotone (symmetricMonoidalPreorder A) (symmetricMonoidalPreorder B) - symmetricMonoidalMonotone F = record - { monoidalMonotone = MP.Free.₁ F.monoidalFunctor - } - where - module F = SymmetricMonoidalFunctor F - - open SymmetricMonoidalNaturalIsomorphism using (⌊_⌋) - - pointwiseIsomorphism - : {F G : SymmetricMonoidalFunctor A B} - → SymmetricMonoidalNaturalIsomorphism F G - → symmetricMonoidalMonotone F ≃ symmetricMonoidalMonotone G - pointwiseIsomorphism F≃G = MP.Free.F-resp-≈ ⌊ F≃G ⌋ - -Free : {o ℓ e : Level} → Functor (SymMonCat {o} {ℓ} {e}) (SymMonPre o ℓ) -Free = record - { F₀ = symmetricMonoidalPreorder - ; F₁ = symmetricMonoidalMonotone - ; identity = λ {A} → ≃.refl {A = symmetricMonoidalPreorder A} {x = id} - ; homomorphism = λ {f = f} {h} → ≃.refl {x = symmetricMonoidalMonotone (∘-SymmetricMonoidal h f)} - ; F-resp-≈ = pointwiseIsomorphism - } - where - open Category (SymMonPre _ _) using (id) - -module Free {o ℓ e} = Functor (Free {o} {ℓ} {e}) |
