diff options
Diffstat (limited to 'Category')
| -rw-r--r-- | Category/Monoidal/Instance/Nat.agda | 37 |
1 files changed, 37 insertions, 0 deletions
diff --git a/Category/Monoidal/Instance/Nat.agda b/Category/Monoidal/Instance/Nat.agda new file mode 100644 index 0000000..9f1b990 --- /dev/null +++ b/Category/Monoidal/Instance/Nat.agda @@ -0,0 +1,37 @@ +{-# OPTIONS --without-K --safe #-} + +module Category.Monoidal.Instance.Nat where + +open import Level using (0ℓ) +open import Categories.Category.Monoidal.Bundle using (MonoidalCategory) +open import Categories.Category.Instance.Nat using (Nat; Nat-Cartesian; Nat-Cocartesian; Natop) +open import Categories.Category.Cartesian using (Cartesian) +open import Categories.Category.Cocartesian using (Cocartesian; module CocartesianMonoidal) +open import Categories.Category.Cartesian.Monoidal using (module CartesianMonoidal) +open import Categories.Category.Duality using (coCartesian⇒Cocartesian; Cocartesian⇒coCartesian) + +open CartesianMonoidal using () renaming (monoidal to ×-monoidal) +open CocartesianMonoidal using (+-monoidal) +open MonoidalCategory + +Natop-Cartesian : Cartesian Natop +Natop-Cartesian = Cocartesian⇒coCartesian Nat Nat-Cocartesian + +Natop-Cocartesian : Cocartesian Natop +Natop-Cocartesian = coCartesian⇒Cocartesian Natop Nat-Cartesian + +Nat,+,0 : MonoidalCategory 0ℓ 0ℓ 0ℓ +Nat,+,0 .U = Nat +Nat,+,0 .monoidal = +-monoidal Nat Nat-Cocartesian + +Nat,×,1 : MonoidalCategory 0ℓ 0ℓ 0ℓ +Nat,×,1 .U = Nat +Nat,×,1 .monoidal = ×-monoidal Nat-Cartesian + +Natop,+,0 : MonoidalCategory 0ℓ 0ℓ 0ℓ +Natop,+,0 .U = Natop +Natop,+,0 .monoidal = ×-monoidal Natop-Cartesian + +Natop,×,1 : MonoidalCategory 0ℓ 0ℓ 0ℓ +Natop,×,1 .U = Natop +Natop,×,1 .monoidal = +-monoidal Natop Natop-Cocartesian |