feat: port CategoryTheory.Additive.Basic

Mathlib.lean

@@ -302,6 +302,7 @@ import Mathlib.Analysis.Subadditive
 import Mathlib.CategoryTheory.Abelian.Basic
 import Mathlib.CategoryTheory.Abelian.Images
 import Mathlib.CategoryTheory.Abelian.NonPreadditive
+import Mathlib.CategoryTheory.Additive.Basic
 import Mathlib.CategoryTheory.Adjunction.Basic
 import Mathlib.CategoryTheory.Adjunction.Comma
 import Mathlib.CategoryTheory.Adjunction.Evaluation

Mathlib/CategoryTheory/Additive/Basic.lean

@@ -0,0 +1,46 @@
+/-
+Copyright (c) 2021 Luke Kershaw. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Luke Kershaw
+
+! This file was ported from Lean 3 source module category_theory.additive.basic
+! leanprover-community/mathlib commit 829895f162a1f29d0133f4b3538f4cd1fb5bffd3
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
+-/
+import Mathlib.CategoryTheory.Preadditive.Basic
+import Mathlib.CategoryTheory.Limits.Shapes.Biproducts
+
+/-!
+# Additive Categories
+
+This file contains the definition of additive categories.
+
+TODO: show that finite biproducts implies enriched over commutative monoids and what is missing
+additionally to have additivity is that identities have additive inverses,
+see https://ncatlab.org/nlab/show/biproduct#BiproductsImplyEnrichment
+-/
+
+
+noncomputable section
+
+open CategoryTheory
+
+open CategoryTheory.Preadditive
+
+open CategoryTheory.Limits
+
+universe v v₀ v₁ v₂ u u₀ u₁ u₂
+
+namespace CategoryTheory
+
+variable (C : Type u) [Category C]
+
+/-- A preadditive category `C` is called additive if it has all finite biproducts.
+See <https://stacks.math.columbia.edu/tag/0104>.
+-/
+class AdditiveCategory extends Preadditive C, HasFiniteBiproducts C
+#align category_theory.additive_category CategoryTheory.AdditiveCategory
+
+end CategoryTheory
+