Theorems · Theorem · group theory
CategoryTheory.Subgroupoid.IsNormal.generatedNormal_le
∀ {C : Type u} [inst : CategoryTheory.Groupoid C] (X : (c d : C) → Set (c ⟶ d)) {S : CategoryTheory.Subgroupoid C},
S.IsNormal → (CategoryTheory.Subgroupoid.generatedNormal X ≤ S ↔ ∀ (c d : C), X c d ⊆ S.arrows c d)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Groupoid
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.
- Setstatement and proof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- LE.le.transproof · cited by 3,151
- CategoryTheory.Groupoidstatement and proof · cited by 182
- sInf_leproof · cited by 110
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.arrowsstatement and proof · cited by 53
- CategoryTheory.Subgroupoid.IsNormalstatement and proof · cited by 15
- CategoryTheory.Subgroupoid.le_iffproof · cited by 3
- CategoryTheory.Subgroupoid.generatedproof · cited by 3
- CategoryTheory.Subgroupoid.generatedNormalstatement and proof · cited by 3
- CategoryTheory.Subgroupoid.generated_le_generatedNormalproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.