Theorems · Definition · group theory
CategoryTheory.Subgroupoid.IsTotallyDisconnected
{C : Type u} → [inst : CategoryTheory.Groupoid C] → CategoryTheory.Subgroupoid C → PropA subgroupoid IsTotallyDisconnected if it has only isotropy arrows.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemproof · cited by 7,166
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.objsproof · cited by 29
- CategoryTheory.Groupoid.IsTotallyDisconnectedproof · cited by 0
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Subgroupoid.isTotallyDisconnected_iffstatement and proof · cited by 1
- CategoryTheory.Subgroupoid.disconnect_isTotallyDisconnectedstatement · cited by 0