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feat: port CategoryTheory.Additive.Basic (#2797)
Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>
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/- | ||
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 | ||
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/-! | ||
# 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 | ||
-/ | ||
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noncomputable section | ||
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open CategoryTheory | ||
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open CategoryTheory.Preadditive | ||
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open CategoryTheory.Limits | ||
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universe v v₀ v₁ v₂ u u₀ u₁ u₂ | ||
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namespace CategoryTheory | ||
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variable (C : Type u) [Category C] | ||
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/-- 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 | ||
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end CategoryTheory | ||
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