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mmontinWhatisRT
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laying out definitions nicely
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formal-spec/CategoricalCrypto/Channel/Category.agda

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@@ -17,18 +17,23 @@ open import abstract-set-theory.Prelude hiding (_⊗_ ; Functor ; Bifunctor)
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opaque
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unfolding _⊗_
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channel-category : Category (sucˡ zeroˡ) zeroˡ zeroˡ
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⊗-bifunctor : Bifunctor channel-category channel-category channel-category
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channel-⊗-monoidal : Monoidal channel-category
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channel-⊗-monoidal-category : MonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
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channel-⊗-braided : Braided channel-⊗-monoidal
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channel-⊗-braided-monoidal-category : BraidedMonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
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channel-⊗-symmetric : Symmetric channel-⊗-monoidal
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channel-category : Category (sucˡ zeroˡ) zeroˡ zeroˡ
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⊗-bifunctor : Bifunctor channel-category channel-category channel-category
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channel-⊗-monoidal : Monoidal channel-category
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channel-⊗-braided : Braided channel-⊗-monoidal
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channel-⊗-symmetric : Symmetric channel-⊗-monoidal
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channel-⊗-monoidal-category : MonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
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channel-⊗-braided-monoidal-category : BraidedMonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
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channel-⊗-symmetric-monoidal-category : SymmetricMonoidalCategory (sucˡ zeroˡ) zeroˡ zeroˡ
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ᵀ-endofunctor : Endofunctor channel-category
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ᵀ-monoidal-functor : MonoidalFunctor channel-⊗-monoidal-category channel-⊗-monoidal-category
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ᵀ-strong-monoidal-functor : StrongMonoidalFunctor channel-⊗-monoidal-category channel-⊗-monoidal-category
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ᵀ-endofunctor : Endofunctor channel-category
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ᵀ-monoidal-functor : MonoidalFunctor channel-⊗-monoidal-category channel-⊗-monoidal-category
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ᵀ-strong-monoidal-functor : StrongMonoidalFunctor channel-⊗-monoidal-category channel-⊗-monoidal-category
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channel-category = categoryHelper record
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{ Obj = Channel
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; _⇒_ = λ A B {m} A [ m ]⇒[ m ] B
@@ -46,7 +51,7 @@ opaque
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; ∘-resp-≈ = λ where
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{h = B⇒C} {A⇒B} f≈B⇒C A⇒B≈i _ trans (f≈B⇒C ∘ A⇒B $ _) (cong B⇒C ∘ A⇒B≈i $ _)
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}
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⊗-bifunctor = record
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{ F₀ = uncurry _⊗_
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; F₁ = λ (A⇒B , C⇒D) ⊗-combine A⇒B C⇒D
@@ -156,7 +161,7 @@ opaque
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_ {Out} (inj₁ _) refl
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_ {Out} (inj₂ _) refl
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_ {In } (inj₁ _) refl
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_ {In } (inj₂ _) refl
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_ {In } (inj₂ _) refl
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}
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; F⇐G = record
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{ η = λ _ ⊗-sym
@@ -169,7 +174,7 @@ opaque
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_ {Out} (inj₁ _) refl
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_ {Out} (inj₂ _) refl
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_ {In } (inj₁ _) refl
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_ {In } (inj₂ _) refl
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_ {In } (inj₂ _) refl
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}
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; iso = λ _ record
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{ isoˡ = λ where
@@ -199,7 +204,7 @@ opaque
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}
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channel-⊗-braided = Symmetric.braided channel-⊗-symmetric
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channel-⊗-symmetric-monoidal-category = record
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{ U = channel-category
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; monoidal = channel-⊗-monoidal
@@ -292,4 +297,3 @@ opaque
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}
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ᵀ-monoidal-functor = StrongMonoidalFunctor.monoidalFunctor ᵀ-strong-monoidal-functor
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