Theorems · Definition · category theory
CategoryTheory.IsArtinianObject
{C : Type u} → [CategoryTheory.Category.{v, u} C] → C → PropAn object X in a category C is Artinian if Subobject X
satisfies the descending chain condition.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.ObjectProperty.Isproof · cited by 4
- CategoryTheory.isArtinianObjectproof · cited by 2
Cited by13
Results whose statement or proof uses this declaration.
- CategoryTheory.isArtinianObject_iff_antitone_chain_conditionstatement · cited by 4
- CategoryTheory.antitone_chain_condition_of_isArtinianObjectstatement and proof · cited by 1
- CategoryTheory.isArtinianObject_iff_isEventuallyConstantstatement · cited by 1
- CategoryTheory.isArtinianObject_iff_not_strictAntistatement and proof · cited by 1
- CategoryTheory.not_strictAnti_of_isArtinianObjectstatement and proof · cited by 0
- CategoryTheory.exists_simple_subobjectstatement and proof · cited by 0
- CategoryTheory.Artinian.casesOnstatement and proof · cited by 0
- CategoryTheory.Artinian.recOnstatement and proof · cited by 0
- CategoryTheory.isArtinianObject_of_isZerostatement · cited by 0
- CategoryTheory.isArtinianObject_of_monostatement and proof · cited by 0
- CategoryTheory.simpleSubobjectstatement and proof · cited by 0
- CategoryTheory.simpleSubobjectArrowstatement and proof · cited by 0