Theorems · Theorem · group theory
CategoryTheory.Subgroupoid.IsWide.wide
∀ {C : Type u} [inst : CategoryTheory.Groupoid C] {S : CategoryTheory.Subgroupoid C},
S.IsWide → ∀ (c : C), CategoryTheory.CategoryStruct.id c ∈ S.arrows c c- 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.
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.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.arrowsstatement · cited by 53
- CategoryTheory.Subgroupoid.IsWidestatement and proof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Subgroupoid.sInf_isNormalproof · cited by 1
- CategoryTheory.Subgroupoid.IsWide.id_memproof · 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.isWide_iff_objs_eq_univproof · cited by 0