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fix line lengths (#44)
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maxsnew authored Jul 22, 2023
1 parent 20158c2 commit eb0ce0a
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18 changes: 11 additions & 7 deletions Cubical/Categories/Constructions/Free/Category/Quiver.agda
Original file line number Diff line number Diff line change
Expand Up @@ -57,7 +57,8 @@ module _ (Q : Quiver ℓg ℓg') where

-- A displayed interpretation
open Categoryᴰ
record Interpᴰ (𝓓 : Categoryᴰ FreeCat ℓd ℓd') : Type ((ℓ-max (ℓ-max ℓg ℓg') (ℓ-max ℓd ℓd'))) where
record Interpᴰ (𝓓 : Categoryᴰ FreeCat ℓd ℓd')
: Type ((ℓ-max (ℓ-max ℓg ℓg') (ℓ-max ℓd ℓd'))) where
field
I-ob : (c : Q .ob) ob[_] 𝓓 c
I-hom : e 𝓓 [ ↑ e ][ I-ob (Q .dom e) , I-ob (Q .cod e) ]
Expand All @@ -69,14 +70,16 @@ module _ (Q : Quiver ℓg ℓg') where
private
module 𝓓 = Categoryᴰ 𝓓

elimF : {c c'} (f : FreeCat [ c , c' ]) 𝓓 [ f ][ ı .I-ob c , ı .I-ob c' ]
elimF : {c c'} (f : FreeCat [ c , c' ])
𝓓 [ f ][ ı .I-ob c , ı .I-ob c' ]
elimF (↑ e) = ı .I-hom e
elimF idₑ = 𝓓 .idᴰ
elimF (f ⋆ₑ g) = elimF f 𝓓.⋆ᴰ elimF g
elimF (⋆ₑIdL f i) = 𝓓 .⋆IdLᴰ (elimF f) i
elimF (⋆ₑIdR f i) = 𝓓 .⋆IdRᴰ (elimF f) i
elimF (⋆ₑAssoc f f₁ f₂ i) = 𝓓 .⋆Assocᴰ (elimF f) (elimF f₁) (elimF f₂) i
elimF (isSetExp f g p q i j) = isOfHLevel→isOfHLevelDep 2 (λ x 𝓓 .isSetHomᴰ)
elimF (isSetExp f g p q i j) =
isOfHLevel→isOfHLevelDep 2 (λ x 𝓓 .isSetHomᴰ)
(elimF f)
(elimF g)
(cong elimF p)
Expand All @@ -103,10 +106,11 @@ module _ (Q : Quiver ℓg ℓg') where
rec ı = Iso.fun (SectionToWkIsoFunctor _ _) (elim ı)

module _ {ℓc ℓc'} {𝓒 : Category ℓc ℓc'} (F G : Functor FreeCat 𝓒)
(agree-on-gen : Interpᴰ (Preorderᴰ→Catᴰ
(SecPath (weaken FreeCat 𝓒)
(Iso.inv (SectionToWkIsoFunctor _ _) F)
(Iso.inv (SectionToWkIsoFunctor _ _) G))))
(agree-on-gen :
Interpᴰ (Preorderᴰ→Catᴰ
(SecPath (weaken FreeCat 𝓒)
(Iso.inv (SectionToWkIsoFunctor _ _) F)
(Iso.inv (SectionToWkIsoFunctor _ _) G))))
where
FreeCatFunctor≡ : F ≡ G
FreeCatFunctor≡ = isoInvInjective (SectionToWkIsoFunctor _ _) F G
Expand Down
18 changes: 11 additions & 7 deletions Cubical/Categories/Displayed/Section.agda
Original file line number Diff line number Diff line change
Expand Up @@ -37,7 +37,8 @@ module _ {C : Category ℓC ℓC'} (D : Categoryᴰ C ℓD ℓD') where
open Section
Section≡ : {F G : Section}
(h : c F .F-ob c ≡ G .F-ob c)
( {c c'} (f : C [ c , c' ]) PathP (λ i D [ f ][ h c i , h c' i ]) (F .F-hom f) (G .F-hom f))
( {c c'} (f : C [ c , c' ])
PathP (λ i D [ f ][ h c i , h c' i ]) (F .F-hom f) (G .F-hom f))
F ≡ G
Section≡ hOb hHom i .F-ob c = hOb c i
Section≡ hOb hHom i .F-hom f = hHom f i
Expand All @@ -47,10 +48,11 @@ module _ {C : Category ℓC ℓC'} (D : Categoryᴰ C ℓD ℓD') where
(G .F-id)
i
Section≡ {F = F}{G = G} hOb hHom i .F-seq f g =
isProp→PathP (λ j D .isSetHomᴰ (hHom (f ⋆⟨ C ⟩ g) j) (hHom f j D.⋆ᴰ hHom g j))
(F .F-seq f g)
(G .F-seq f g)
i
isProp→PathP
(λ j D .isSetHomᴰ (hHom (f ⋆⟨ C ⟩ g) j) (hHom f j D.⋆ᴰ hHom g j))
(F .F-seq f g)
(G .F-seq f g)
i

SectionToFunctor : Section Functor C (∫C D)
SectionToFunctor F .F-ob x = x , F .F-ob x
Expand Down Expand Up @@ -88,14 +90,16 @@ open Preorder.Section
module _ (C : Category ℓC ℓC') (P : Preorderᴰ C ℓD ℓD') where
open Iso
open Preorderᴰ
PreorderSectionIsoCatSection : Iso (Preorder.Section P) (Section (Preorderᴰ→Catᴰ P))
PreorderSectionIsoCatSection
: Iso (Preorder.Section P) (Section (Preorderᴰ→Catᴰ P))
PreorderSectionIsoCatSection .fun F .F-ob = F .F-ob
PreorderSectionIsoCatSection .fun F .F-hom = F .F-hom
PreorderSectionIsoCatSection .fun F .F-id = P .isPropHomᴰ _ _
PreorderSectionIsoCatSection .fun F .F-seq f g = P .isPropHomᴰ _ _
PreorderSectionIsoCatSection .inv F .F-ob = F .F-ob
PreorderSectionIsoCatSection .inv F .F-hom = F .F-hom
PreorderSectionIsoCatSection .rightInv b = Section≡ _ (λ c refl) (λ f refl)
PreorderSectionIsoCatSection .rightInv b =
Section≡ _ (λ c refl) (λ f refl)
PreorderSectionIsoCatSection .leftInv a = refl

module _ (C : Category ℓC ℓC') (D : Category ℓD ℓD') where
Expand Down

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