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Theorems · Definition · category theory

CategoryTheory.Indecomposable

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → [CategoryTheory.Limits.HasBinaryBiproducts C] → C → Prop

An object is indecomposable if it cannot be written as the biproduct of two nonzero objects.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproducts
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CategoryTheory.indecomposable_of_simple · cited by 0CategoryTheory.indecompos…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.biprod · cited by 312Limits.biprodCategoryTheory.Limits.IsZero · cited by 306Limits.IsZeroCategoryTheory.Limits.HasBinaryBiproducts · cited by 165Limits.HasBinaryBiproductsCategoryTheory.IndecomposableCITED BYCITES

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