Theorems · Theorem · group theory
CategoryTheory.Subgroupoid.IsNormal.conj
∀ {C : Type u} [inst : CategoryTheory.Groupoid C] {S : CategoryTheory.Subgroupoid C},
S.IsNormal →
∀ {c d : C} (p : c ⟶ d) {γ : c ⟶ c},
γ ∈ S.arrows c c →
CategoryTheory.CategoryStruct.comp (CategoryTheory.Groupoid.inv p) (CategoryTheory.CategoryStruct.comp γ p) ∈
S.arrows d d- Cited by
- 6 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Groupoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.arrowsstatement · cited by 53
- CategoryTheory.Groupoid.invstatement · cited by 36
- CategoryTheory.Subgroupoid.IsNormalstatement and proof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Subgroupoid.IsNormal.conj'proof · cited by 2
- CategoryTheory.Subgroupoid.sInf_isNormalproof · cited by 1
- CategoryTheory.Subgroupoid.isNormal_comapproof · cited by 1
- CategoryTheory.Subgroupoid.disconnect_normalproof · cited by 0
- CategoryTheory.Subgroupoid.isNormal_mapproof · cited by 0
- CategoryTheory.Subgroupoid.IsNormal.conjugation_bijproof · cited by 0