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-rw-r--r--Morphism/SplitIdempotent.agda22
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+{-# OPTIONS --without-K --safe #-}
+
+open import Level using (Level; _⊔_)
+open import Categories.Category using (Category)
+
+module Morphism.SplitIdempotent {o ℓ e : Level} (𝒞 : Category o ℓ e) where
+
+open Category 𝒞
+
+record IsSplitIdempotent {A : Obj} (i : A ⇒ A) : Set (o ⊔ ℓ ⊔ e) where
+ field
+ B : Obj
+ r : A ⇒ B
+ s : B ⇒ A
+ s∘r : s ∘ r ≈ i
+ r∘s : r ∘ s ≈ id
+
+record SplitIdempotent : Set (o ⊔ ℓ ⊔ e) where
+ field
+ {A} : Obj
+ i : A ⇒ A
+ isSplitIdempotent : IsSplitIdempotent i