Theorems · Theorem · group theory
Subgroup.comap_map_eq_self
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N} {H : Subgroup G},
f.ker ≤ H → Subgroup.comap f (Subgroup.map f H) = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- MonoidHom.kerstatement and proof · cited by 212
- Subgroup.comapstatement · cited by 154
- sup_eq_leftproof · cited by 71
- Subgroup.comap_map_eqproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.comap_map_eq_self_of_injectiveproof · cited by 7
- Group.normalizerCondition_of_isNilpotentproof · cited by 2
- Subgroup.isCoatom_comap_of_surjectiveproof · cited by 1
- Subgroup.goursatproof · cited by 0