Add categories with all binary biproducts

1 files changed, 13 insertions, 0 deletions

diff --git a/Morphism/Zero.agda b/Morphism/Zero.agda
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+++ b/Morphism/Zero.agda
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+{-# OPTIONS --without-K --safe #-}
+
+open import Categories.Category using (Category)
+open import Level using (Level; _⊔_)
+
+module Morphism.Zero {o ℓ e : Level} (𝒞 : Category o ℓ e) where
+
+open Category 𝒞
+
+record IsZero⇒ {A B : Obj} (z : A ⇒ B) : Set (o ⊔ ℓ ⊔ e) where
+  field
+    constant : {C : Obj} (f g : C ⇒ A) → z ∘ f ≈ z ∘ g
+    coconstant : {C : Obj} (f g : B ⇒ C) → f ∘ z ≈ g ∘ z