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{-# OPTIONS --without-K --safe #-}
open import Level using (Level)
module Category.Instance.One.Properties {o ℓ e : Level} where
open import Categories.Category.Core using (Category)
open import Categories.Category.Instance.One using () renaming (One to One′)
One : Category o ℓ e
One = One′
open import Categories.Category.Cocartesian One using (Cocartesian)
open import Categories.Category.Cocomplete.Finitely One using (FinitelyCocomplete)
open import Categories.Object.Initial One using (Initial)
open import Categories.Category.Cocartesian One using (BinaryCoproducts)
One-Initial : Initial
One-Initial = _
One-BinaryCoproducts : BinaryCoproducts
One-BinaryCoproducts = _
One-Cocartesian : Cocartesian
One-Cocartesian = record
{ initial = One-Initial
; coproducts = One-BinaryCoproducts
}
One-FinitelyCocomplete : FinitelyCocomplete
One-FinitelyCocomplete = record
{ cocartesian = One-Cocartesian
; coequalizer = _
}
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