diff options
| -rw-r--r-- | Category/Instance/Setoids/SymmetricMonoidal.agda | 16 |
1 files changed, 14 insertions, 2 deletions
diff --git a/Category/Instance/Setoids/SymmetricMonoidal.agda b/Category/Instance/Setoids/SymmetricMonoidal.agda index 8f448dc..f21124e 100644 --- a/Category/Instance/Setoids/SymmetricMonoidal.agda +++ b/Category/Instance/Setoids/SymmetricMonoidal.agda @@ -17,11 +17,23 @@ open import Categories.Category.Cocartesian (Setoids c (c ⊔ ℓ)) open CocartesianMonoidal (Setoids-Cocartesian {c} {ℓ}) using (+-monoidal) open CocartesianSymmetricMonoidal (Setoids-Cocartesian {c} {ℓ}) using (+-symmetric) +open import Categories.Category using (Category) +open import Categories.Category.Monoidal using (Monoidal) +open import Categories.Category.Monoidal.Symmetric using (Symmetric) + +opaque + + ×-monoidal′ : Monoidal (Setoids c ℓ) + ×-monoidal′ = ×-monoidal {c} {ℓ} + + ×-symmetric′ : Symmetric ×-monoidal′ + ×-symmetric′ = ×-symmetric + Setoids-× : SymmetricMonoidalCategory (suc (c ⊔ ℓ)) (c ⊔ ℓ) (c ⊔ ℓ) Setoids-× = record { U = Setoids c ℓ - ; monoidal = ×-monoidal - ; symmetric = ×-symmetric + ; monoidal = ×-monoidal′ + ; symmetric = ×-symmetric′ } Setoids-+ : SymmetricMonoidalCategory (suc (c ⊔ ℓ)) (c ⊔ ℓ) (c ⊔ ℓ) |