@@ -17,18 +17,23 @@ open import abstract-set-theory.Prelude hiding (_⊗_ ; Functor ; Bifunctor)
1717opaque
1818 unfolding _⊗_
1919
20- channel-category : Category (sucˡ zeroˡ) zeroˡ zeroˡ
21- ⊗-bifunctor : Bifunctor channel-category channel-category channel-category
22- channel-⊗-monoidal : Monoidal channel-category
23- channel-⊗-monoidal-category : MonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
24- channel-⊗-braided : Braided channel-⊗-monoidal
25- channel-⊗-braided-monoidal-category : BraidedMonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
26- channel-⊗-symmetric : Symmetric channel-⊗-monoidal
20+ channel-category : Category (sucˡ zeroˡ) zeroˡ zeroˡ
21+
22+ ⊗-bifunctor : Bifunctor channel-category channel-category channel-category
23+
24+ channel-⊗-monoidal : Monoidal channel-category
25+ channel-⊗-braided : Braided channel-⊗-monoidal
26+ channel-⊗-symmetric : Symmetric channel-⊗-monoidal
27+
28+ channel-⊗-monoidal-category : MonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
29+ channel-⊗-braided-monoidal-category : BraidedMonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
2730 channel-⊗-symmetric-monoidal-category : SymmetricMonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
28- ᵀ-endofunctor : Endofunctor channel-category
29- ᵀ-monoidal-functor : MonoidalFunctor channel-⊗-monoidal-category channel-⊗-monoidal-category
30- ᵀ-strong-monoidal-functor : StrongMonoidalFunctor channel-⊗-monoidal-category channel-⊗-monoidal-category
31-
31+
32+ ᵀ-endofunctor : Endofunctor channel-category
33+
34+ ᵀ-monoidal-functor : MonoidalFunctor channel-⊗-monoidal-category channel-⊗-monoidal-category
35+ ᵀ-strong-monoidal-functor : StrongMonoidalFunctor channel-⊗-monoidal-category channel-⊗-monoidal-category
36+
3237 channel-category = categoryHelper record
3338 { Obj = Channel
3439 ; _⇒_ = λ A B → ∀ {m} → A [ m ]⇒[ m ] B
4651 ; ∘-resp-≈ = λ where
4752 {h = B⇒C} {A⇒B} f≈B⇒C A⇒B≈i _ → trans (f≈B⇒C ∘ A⇒B $ _) (cong B⇒C ∘ A⇒B≈i $ _)
4853 }
49-
54+
5055 ⊗-bifunctor = record
5156 { F₀ = uncurry _⊗_
5257 ; F₁ = λ (A⇒B , C⇒D) → ⊗-combine A⇒B C⇒D
@@ -156,7 +161,7 @@ opaque
156161 _ {Out} (inj₁ _) → refl
157162 _ {Out} (inj₂ _) → refl
158163 _ {In } (inj₁ _) → refl
159- _ {In } (inj₂ _) → refl
164+ _ {In } (inj₂ _) → refl
160165 }
161166 ; F⇐G = record
162167 { η = λ _ → ⊗-sym
@@ -169,7 +174,7 @@ opaque
169174 _ {Out} (inj₁ _) → refl
170175 _ {Out} (inj₂ _) → refl
171176 _ {In } (inj₁ _) → refl
172- _ {In } (inj₂ _) → refl
177+ _ {In } (inj₂ _) → refl
173178 }
174179 ; iso = λ _ → record
175180 { isoˡ = λ where
@@ -199,7 +204,7 @@ opaque
199204 }
200205
201206 channel-⊗-braided = Symmetric.braided channel-⊗-symmetric
202-
207+
203208 channel-⊗-symmetric-monoidal-category = record
204209 { U = channel-category
205210 ; monoidal = channel-⊗-monoidal
@@ -292,4 +297,3 @@ opaque
292297 }
293298
294299 ᵀ-monoidal-functor = StrongMonoidalFunctor.monoidalFunctor ᵀ-strong-monoidal-functor
295-
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