Theorems · Definition · group theory
CategoryTheory.Subgroupoid.vertexSubgroup
{C : Type u} →
[inst : CategoryTheory.Groupoid C] → (S : CategoryTheory.Subgroupoid C) → {c : C} → c ∈ S.objs → Subgroup (c ⟶ c)The subgroup of the vertex group at c given by the subgroupoid
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 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.
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- Subgroupstatement · cited by 3,593
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.arrowsproof · cited by 53
- CategoryTheory.Subgroupoid.objsstatement and proof · cited by 29
- CategoryTheory.Subgroupoid.invproof · cited by 6
- CategoryTheory.Subgroupoid.mulproof · cited by 5
- CategoryTheory.Subgroupoid.id_mem_of_nonempty_isotropyproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Subgroupoid.IsNormal.vertexSubgroupstatement and proof · cited by 0