diff --git a/src/Categories/Category/Cocartesian.agda b/src/Categories/Category/Cocartesian.agda index 92de6a7b0..28b6d38f0 100644 --- a/src/Categories/Category/Cocartesian.agda +++ b/src/Categories/Category/Cocartesian.agda @@ -29,6 +29,7 @@ open import Categories.Morphism 𝒞 open import Categories.Morphism.Properties 𝒞 open import Categories.Morphism.Duality 𝒞 open import Categories.Morphism.Reasoning 𝒞 +open import Categories.NaturalTransformation.NaturalIsomorphism using (NaturalIsomorphism) open import Categories.Object.Initial 𝒞 using (Initial) open import Categories.Object.Coproduct 𝒞 open import Categories.Object.Duality 𝒞 @@ -149,11 +150,14 @@ module CocartesianMonoidal (cocartesian : Cocartesian) where A+⊥≅A : A + ⊥ ≅ A A+⊥≅A = op-≅⇒≅ (op-cartesianMonoidal.A×⊤≅A) - open op-cartesianMonoidal - using (monoidal) - -- both are natural isomorphism - renaming (⊤×--id to ⊥+--id; -×⊤-id to -+⊥-id) - public + open op-cartesianMonoidal using (monoidal; ⊤×--id; -×⊤-id) + open NaturalIsomorphism using (op′) + + ⊥+--id : NaturalIsomorphism (⊥ +-) idF + ⊥+--id = op′ ⊤×--id + + -+⊥-id : NaturalIsomorphism (-+ ⊥) idF + -+⊥-id = op′ -×⊤-id open Monoidal monoidal using (unit; unitorˡ-commute-to; unitorˡ-commute-from; unitorʳ-commute-to; unitorʳ-commute-from; assoc-commute-to; assoc-commute-from; triangle; pentagon)