Theorems · Theorem · category theory
CategoryTheory.isNoetherianObject_iff_not_strictMono
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (X : C),
CategoryTheory.IsNoetherianObject X ↔ ∀ (f : ℕ → CategoryTheory.Subobject X), ¬StrictMono f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 37 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.
Cites13
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
- StrictMonostatement and proof · cited by 706
- CategoryTheory.Subobjectstatement and proof · cited by 385
- RelEmbeddingproof · cited by 281
- RelEmbedding.toEmbeddingproof · cited by 45
- RelEmbedding.map_rel_iffproof · cited by 25
- Function.Embedding.toFunproof · cited by 25
- isWellFounded_iffproof · cited by 9
- CategoryTheory.IsNoetherianObjectstatement and proof · cited by 8
- CategoryTheory.ObjectProperty.is_iffproof · cited by 6
- RelEmbedding.wellFounded_iff_isEmptyproof · cited by 4
- CategoryTheory.isNoetherianObjectproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.not_strictMono_of_isNoetherianObjectproof · cited by 0