Theorems · Theorem · group theory
CategoryTheory.Subgroupoid.le_iff
∀ {C : Type u} [inst : CategoryTheory.Groupoid C] (S T : CategoryTheory.Subgroupoid C),
S ≤ T ↔ ∀ {c d : C}, S.arrows c d ⊆ T.arrows c d- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Groupoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Groupoidstatement and proof · cited by 182
- SetLike.le_defproof · cited by 76
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.arrowsstatement and proof · cited by 53
- Sigma.forallproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Subgroupoid.disconnect_leproof · cited by 0
- CategoryTheory.Subgroupoid.full_monoproof · cited by 0
- CategoryTheory.Subgroupoid.IsNormal.generatedNormal_leproof · cited by 0