Theorems · Theorem · group theory
CategoryTheory.Subgroupoid.mem_objs_of_src
∀ {C : Type u} [inst : CategoryTheory.Groupoid C] (S : CategoryTheory.Subgroupoid C) {c d : C} {f : c ⟶ d},
f ∈ S.arrows c d → c ∈ S.objs- Cited by
- 4 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- 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
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Subgroupoidstatement and proof · cited by 75
- CategoryTheory.Subgroupoid.arrowsstatement and proof · cited by 53
- CategoryTheory.Groupoid.invproof · cited by 36
- CategoryTheory.Subgroupoid.objsstatement · cited by 29
- CategoryTheory.Subgroupoid.invproof · cited by 6
- CategoryTheory.Subgroupoid.mulproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Subgroupoid.mem_map_objs_iffproof · cited by 1
- CategoryTheory.Subgroupoid.isTotallyDisconnected_iffproof · cited by 1
- CategoryTheory.Subgroupoid.id_mem_of_srcproof · cited by 1
- CategoryTheory.Subgroupoid.isWide_iff_objs_eq_univproof · cited by 0