Skip to content

Add functors between (co)cone categories #448

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
JacquesCarette merged 1 commit into from
Jan 29, 2025
Merged

Add functors between (co)cone categories #448

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
32 changes: 31 additions & 1 deletion src/Categories/Diagram/Cocone/Properties.agda
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -8,8 +8,9 @@ open import Categories.Category
open import Categories.Functor
open import Categories.Functor.Properties
open import Categories.NaturalTransformation
open import Categories.Diagram.Cone.Properties
open import Categories.Diagram.Cone.Properties using (F-map-Coneʳ; F-map-Cone⇒ʳ; nat-map-Cone; nat-map-Cone⇒)
open import Categories.Diagram.Duality
open import Categories.Category.Construction.Cocones using (Cocones)

import Categories.Diagram.Cocone as Coc
import Categories.Morphism.Reasoning as MR
Expand Down Expand Up @@ -45,6 +46,15 @@ module _ {F : Functor J C} (G : Functor C D) where
}
where open CF.Cocone⇒ f

mapˡ : Functor (Cocones F) (Cocones (G ∘F F))
mapˡ = record
{ F₀ = F-map-Coconeˡ
; F₁ = F-map-Cocone⇒ˡ
; identity = G.identity
; homomorphism = G.homomorphism
; F-resp-≈ = G.F-resp-≈
}

module _ {F : Functor J C} (G : Functor J′ J) where
private
module C = Category C
Expand All @@ -61,8 +71,19 @@ module _ {F : Functor J C} (G : Functor J′ J) where
F-map-Cocone⇒ʳ : ∀ {K K′} (f : CF.Cocone⇒ K K′) → CFG.Cocone⇒ (F-map-Coconeʳ K) (F-map-Coconeʳ K′)
F-map-Cocone⇒ʳ f = coCone⇒⇒Cocone⇒ C (F-map-Cone⇒ʳ G.op (Cocone⇒⇒coCone⇒ C f))

mapʳ : Functor (Cocones F) (Cocones (F ∘F G))
mapʳ = record
{ F₀ = F-map-Coconeʳ
; F₁ = F-map-Cocone⇒ʳ
; identity = C.Equiv.refl
; homomorphism = C.Equiv.refl
; F-resp-≈ = λ f≈g → f≈g
}


module _ {F G : Functor J C} (α : NaturalTransformation F G) where
private
module C = Category C
module α = NaturalTransformation α
module CF = Coc F
module CG = Coc G
Expand All @@ -72,3 +93,12 @@ module _ {F G : Functor J C} (α : NaturalTransformation F G) where

nat-map-Cocone⇒ : ∀ {K K′} (f : CG.Cocone⇒ K K′) → CF.Cocone⇒ (nat-map-Cocone K) (nat-map-Cocone K′)
nat-map-Cocone⇒ f = coCone⇒⇒Cocone⇒ C (nat-map-Cone⇒ α.op (Cocone⇒⇒coCone⇒ C f))

nat-map : Functor (Cocones G) (Cocones F)
nat-map = record
{ F₀ = nat-map-Cocone
; F₁ = nat-map-Cocone⇒
; identity = C.Equiv.refl
; homomorphism = C.Equiv.refl
; F-resp-≈ = λ f≈g → f≈g
}
28 changes: 28 additions & 0 deletions src/Categories/Diagram/Cone/Properties.agda
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -10,6 +10,7 @@ open import Categories.Functor.Properties
open import Categories.NaturalTransformation
import Categories.Diagram.Cone as Con
import Categories.Morphism.Reasoning as MR
open import Categories.Category.Construction.Cones using (Cones)

private
variable
Expand Down Expand Up @@ -42,6 +43,15 @@ module _ {F : Functor J C} (G : Functor C D) where
}
where open CF.Cone⇒ f

mapˡ : Functor (Cones F) (Cones (G ∘F F))
mapˡ = record
{ F₀ = F-map-Coneˡ
; F₁ = F-map-Cone⇒ˡ
; identity = G.identity
; homomorphism = G.homomorphism
; F-resp-≈ = G.F-resp-≈
}

module _ {F : Functor J C} (G : Functor J′ J) where
private
module C = Category C
Expand All @@ -68,6 +78,15 @@ module _ {F : Functor J C} (G : Functor J′ J) where
}
where open CF.Cone⇒ f

mapʳ : Functor (Cones F) (Cones (F ∘F G))
mapʳ = record
{ F₀ = F-map-Coneʳ
; F₁ = F-map-Cone⇒ʳ
; identity = C.Equiv.refl
; homomorphism = C.Equiv.refl
; F-resp-≈ = λ f≈g → f≈g
}

module _ {F G : Functor J C} (α : NaturalTransformation F G) where
private
module C = Category C
Expand Down Expand Up @@ -99,3 +118,12 @@ module _ {F G : Functor J C} (α : NaturalTransformation F G) where
; commute = pullʳ commute
}
where open CF.Cone⇒ f

nat-map : Functor (Cones F) (Cones G)
nat-map = record
{ F₀ = nat-map-Cone
; F₁ = nat-map-Cone⇒
; identity = C.Equiv.refl
; homomorphism = C.Equiv.refl
; F-resp-≈ = λ f≈g → f≈g
}
Loading