Theorems · Definition · category theory

CategoryTheory.simpleSubobject

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.Limits.HasZeroMorphisms C] →
      [CategoryTheory.Limits.HasZeroObject C] →
        {X : C} → [CategoryTheory.IsArtinianObject X] → ¬CategoryTheory.Limits.IsZero X → C

Choose an arbitrary simple subobject of a non-zero Artinian object.

Defined in

Mathlib.CategoryTheory.Subobject.ArtinianObject

Cited by

0 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectCategoryTheory.IsArtinianObject