Theorems · Theorem · category theory

CategoryTheory.indecomposable_of_simple

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] (X : C) [CategoryTheory.Simple X],
  CategoryTheory.Indecomposable X

Any simple object in a preadditive category is indecomposable.

Defined in

Mathlib.CategoryTheory.Simple

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproductsCategoryTheory.Simple