Theorems · Theorem · category theory

CategoryTheory.exists_simple_subobject

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [CategoryTheory.Limits.HasZeroObject C] {X : C} [CategoryTheory.IsArtinianObject X],
  ¬CategoryTheory.Limits.IsZero X → ∃ Y, CategoryTheory.Simple (CategoryTheory.Subobject.underlying.obj Y)

Defined in

Mathlib.CategoryTheory.Subobject.ArtinianObject

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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