diff options
Diffstat (limited to 'Functor/Exact/Instance/Swap.agda')
| -rw-r--r-- | Functor/Exact/Instance/Swap.agda | 10 |
1 files changed, 4 insertions, 6 deletions
diff --git a/Functor/Exact/Instance/Swap.agda b/Functor/Exact/Instance/Swap.agda index 99a27c5..98ca0f4 100644 --- a/Functor/Exact/Instance/Swap.agda +++ b/Functor/Exact/Instance/Swap.agda @@ -6,28 +6,26 @@ open import Category.Cocomplete.Finitely.Bundle using (FinitelyCocompleteCategor module Functor.Exact.Instance.Swap {o β e : Level} (π π : FinitelyCocompleteCategory o β e) where open import Categories.Category using (_[_,_]) -open import Categories.Category.BinaryProducts using (BinaryProducts) open import Categories.Category.Product using (Product) renaming (Swap to Swapβ²) open import Categories.Category.Cartesian using (Cartesian) open import Categories.Diagram.Coequalizer using (IsCoequalizer) open import Categories.Object.Initial using (IsInitial) open import Categories.Object.Coproduct using (IsCoproduct) -open import Data.Product.Base using (_,_; projβ; projβ; swap) +open import Data.Product using (_,_; projβ; projβ; swap) open import Category.Instance.FinitelyCocompletes {o} {β} {e} using (FinitelyCocompletes-Cartesian) open import Functor.Exact using (RightExactFunctor) module FCC = Cartesian FinitelyCocompletes-Cartesian -open BinaryProducts (FCC.products) using (_Γ_) -- ; Οβ; Οβ; _β_; assocΛ‘) - +open FCC using (_Γ_) module π = FinitelyCocompleteCategory π module π = FinitelyCocompleteCategory π swap-resp-β₯ : {A : π.Obj} {B : π.Obj} β IsInitial (Product π.U π.U) (A , B) β IsInitial (Product π.U π.U) (B , A) swap-resp-β₯ {A} {B} isInitial = record - { ! = swap ! - ; !-unique = Ξ» { (f , g) β swap (!-unique (g , f)) } + { Β‘ = swap Β‘ + ; Β‘-unique = Ξ» { (f , g) β swap (Β‘-unique (g , f)) } } where open IsInitial isInitial |
