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14 changes: 9 additions & 5 deletions src/Categories/Category/Cocartesian.agda
Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand Down Expand Up @@ -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)
Expand Down
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