Theorems · Theorem · group theory
Subgroup.comap_eq_ker
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N} {H : Subgroup N},
Subgroup.comap f H = f.ker ↔ Disjoint H f.range- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Bot.botproof · cited by 4,720
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Disjointstatement and proof · cited by 2,201
- MonoidHom.rangestatement and proof · cited by 314
- MonoidHom.kerstatement · cited by 212
- Subgroup.comapstatement and proof · cited by 154
- inf_commproof · cited by 139
- disjoint_iffproof · cited by 76
- LE.le.ge_iff_eq'proof · cited by 50
- Subgroup.map_eq_bot_iffproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.comap_eq_ker_of_surjectiveproof · cited by 1