Theorems · Theorem · group theory
CategoryTheory.Subgroupoid.isTotallyDisconnected_iff
∀ {C : Type u} [inst : CategoryTheory.Groupoid C] (S : CategoryTheory.Subgroupoid C),
S.IsTotallyDisconnected ↔ ∀ (c d : C), (S.arrows c d).Nonempty → c = d- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- Set.Elemproof · cited by 7,166
- Set.Nonemptystatement and proof · cited by 2,627
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.arrowsstatement and proof · cited by 53
- CategoryTheory.Subgroupoid.objsproof · cited by 29
- CategoryTheory.Subgroupoid.mem_objs_of_srcproof · cited by 4
- CategoryTheory.Subgroupoid.IsTotallyDisconnectedstatement and proof · cited by 2
- CategoryTheory.Subgroupoid.mem_objs_of_tgtproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Subgroupoid.disconnect_isTotallyDisconnectedproof · cited by 0