# HG changeset patch # User Shinji KONO # Date 1509355116 -32400 # Node ID 959954fc29f86197ce99275d9d8c9890dae399c6 # Parent 99065a1e56eaf96ccd5519a7580d3313f9d29d7a fix diff -r 99065a1e56ea -r 959954fc29f8 freyd.agda --- a/freyd.agda Mon Oct 30 18:14:41 2017 +0900 +++ b/freyd.agda Mon Oct 30 18:18:36 2017 +0900 @@ -30,11 +30,11 @@ preinitialArrow : ∀{a : Obj A } → Hom A ( FObj F preinitialObj ) a -- initial object - -record HasInitialObject {c₁ c₂ ℓ : Level} (A : Category c₁ c₂ ℓ) (i : Obj A) : Set (suc ℓ ⊔ (suc c₁ ⊔ suc c₂)) where - field - initial : ∀( a : Obj A ) → Hom A i a - uniqueness : { a : Obj A } → ( f : Hom A i a ) → A [ f ≈ initial a ] +-- now in cat-utility +-- record HasInitialObject {c₁ c₂ ℓ : Level} (A : Category c₁ c₂ ℓ) (i : Obj A) : Set (suc ℓ ⊔ (suc c₁ ⊔ suc c₂)) where +-- field +-- initial : ∀( a : Obj A ) → Hom A i a +-- uniqueness : { a : Obj A } → ( f : Hom A i a ) → A [ f ≈ initial a ] -- A complete catagory has initial object if it has PreInitial-SmallFullSubcategory