diff options
Diffstat (limited to 'Category/Instance')
| -rw-r--r-- | Category/Instance/Cospans.agda | 15 | ||||
| -rw-r--r-- | Category/Instance/DecoratedCospans.agda | 9 |
2 files changed, 12 insertions, 12 deletions
diff --git a/Category/Instance/Cospans.agda b/Category/Instance/Cospans.agda index 0dee26c..d54499d 100644 --- a/Category/Instance/Cospans.agda +++ b/Category/Instance/Cospans.agda @@ -10,7 +10,7 @@ module Category.Instance.Cospans {o ℓ e} (𝒞 : FinitelyCocompleteCategory o open FinitelyCocompleteCategory 𝒞 open import Categories.Diagram.Pushout U using (Pushout) -open import Categories.Diagram.Pushout.Properties U using (pushout-resp-≈) +open import Categories.Diagram.Pushout.Properties U using (pushout-resp-≈; up-to-iso) open import Categories.Morphism U using (_≅_; module ≅) open import Categories.Morphism.Reasoning U using @@ -22,7 +22,6 @@ open import Categories.Morphism.Reasoning U open import Category.Diagram.Pushout U using ( glue-i₁ ; glue-i₂ - ; up-to-iso ; pushout-f-id ; pushout-id-g ; extend-i₁-iso ; extend-i₂-iso ) @@ -47,8 +46,8 @@ compose c₁ c₂ = record { f₁ = p.i₁ ∘ C₁.f₁ ; f₂ = p.i₂ ∘ C module C₂ = Cospan c₂ module p = pushout C₁.f₂ C₂.f₁ -identity : Cospan A A -identity = record { f₁ = id ; f₂ = id } +id-Cospan : Cospan A A +id-Cospan = record { f₁ = id ; f₂ = id } compose-3 : Cospan A B → Cospan B C → Cospan C D → Cospan A D compose-3 c₁ c₂ c₃ = record { f₁ = P₃.i₁ ∘ P₁.i₁ ∘ C₁.f₁ ; f₂ = P₃.i₂ ∘ P₂.i₂ ∘ C₃.f₂ } @@ -101,7 +100,7 @@ same-trans C≈C′ C′≈C″ = record module C≈C′ = Same C≈C′ module C′≈C″ = Same C′≈C″ -compose-idˡ : {C : Cospan A B} → Same (compose C identity) C +compose-idˡ : {C : Cospan A B} → Same (compose C id-Cospan) C compose-idˡ {_} {_} {C} = record { ≅N = ≅P ; from∘f₁≈f₁′ = begin @@ -123,7 +122,7 @@ compose-idˡ {_} {_} {C} = record ≅P = up-to-iso P P′ module ≅P = _≅_ ≅P -compose-idʳ : {C : Cospan A B} → Same (compose identity C) C +compose-idʳ : {C : Cospan A B} → Same (compose id-Cospan C) C compose-idʳ {_} {_} {C} = record { ≅N = ≅P ; from∘f₁≈f₁′ = begin @@ -145,7 +144,7 @@ compose-idʳ {_} {_} {C} = record ≅P = up-to-iso P P′ module ≅P = _≅_ ≅P -compose-id² : Same {A} (compose identity identity) identity +compose-id² : Same {A} (compose id-Cospan id-Cospan) id-Cospan compose-id² = compose-idˡ compose-3-right @@ -264,7 +263,7 @@ Cospans = record { Obj = Obj ; _⇒_ = Cospan ; _≈_ = Same - ; id = identity + ; id = id-Cospan ; _∘_ = flip compose ; assoc = compose-assoc ; sym-assoc = compose-sym-assoc diff --git a/Category/Instance/DecoratedCospans.agda b/Category/Instance/DecoratedCospans.agda index 3f9b6ee..c0c62c7 100644 --- a/Category/Instance/DecoratedCospans.agda +++ b/Category/Instance/DecoratedCospans.agda @@ -23,6 +23,7 @@ import Category.Instance.Cospans 𝒞 as Cospans open import Categories.Category using (Category; _[_∘_]) open import Categories.Category.Cocartesian using (module CocartesianMonoidal) open import Categories.Diagram.Pushout using (Pushout) +open import Categories.Diagram.Pushout.Properties 𝒞.U using (up-to-iso) open import Categories.Functor.Properties using ([_]-resp-≅) open import Categories.Morphism.Reasoning using (switch-fromtoˡ; glueTrianglesˡ) open import Cospan.Decorated 𝒞 F using (DecoratedCospan) @@ -30,7 +31,7 @@ open import Data.Product using (_,_) open import Function using (flip) open import Level using (_⊔_) -open import Category.Diagram.Pushout 𝒞.U using (glue-i₁; glue-i₂; pushout-id-g; pushout-f-id; up-to-iso) +open import Category.Diagram.Pushout 𝒞.U using (glue-i₁; glue-i₂; pushout-id-g; pushout-f-id) import Category.Monoidal.Coherence as Coherence @@ -66,7 +67,7 @@ compose c₁ c₂ = record identity : DecoratedCospan A A identity = record - { cospan = Cospans.identity + { cospan = Cospans.id-Cospan ; decoration = 𝒟.U [ F₁ 𝒞.initial.! ∘ ε ] } @@ -629,8 +630,8 @@ compose-equiv {_} {_} {_} {c₂} {c₂′} {c₁} {c₁′} ≅C₂ ≅C₁ = re F₁ [ P′.i₁ , P′.i₂ ] ∘ φ (N′ , M′) ∘ (F₁ N⇒ ∘ s) ⊗₁ (F₁ M⇒ ∘ t) ∘ ρ⇐ ≈⟨ refl⟩∘⟨ refl⟩∘⟨ ≅C₁.same-deco ⟩⊗⟨ ≅C₂.same-deco ⟩∘⟨refl ⟩ F₁ [ P′.i₁ , P′.i₂ ] ∘ φ (N′ , M′) ∘ s′ ⊗₁ t′ ∘ ρ⇐ ∎ -Cospans : Category o (o ⊔ ℓ ⊔ ℓ′) (ℓ ⊔ e ⊔ e′) -Cospans = record +DecoratedCospans : Category o (o ⊔ ℓ ⊔ ℓ′) (ℓ ⊔ e ⊔ e′) +DecoratedCospans = record { Obj = 𝒞.Obj ; _⇒_ = DecoratedCospan ; _≈_ = Same |