Theorems · Theorem · group theory
Subgroup.map_comap_eq_self
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N} {H : Subgroup N},
H ≤ f.range → Subgroup.map f (Subgroup.comap f H) = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 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
- MonoidHom.rangestatement and proof · cited by 314
- Subgroup.mapstatement · cited by 301
- Subgroup.comapstatement · cited by 154
- inf_eq_rightproof · cited by 64
- Subgroup.map_comap_eqproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.map_comap_eq_self_of_surjectiveproof · cited by 3
- Subgroup.comap_normalizer_eq_of_le_rangeproof · cited by 2
- Subgroup.comap_le_comap_of_le_rangeproof · cited by 1