Theorems · Theorem · group theory
Subgroup.map_comap_eq_self_of_surjective
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N},
Function.Surjective ⇑f → ∀ (H : Subgroup N), Subgroup.map f (Subgroup.comap f H) = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 3 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- le_topproof · cited by 411
- Subgroup.mapstatement · cited by 301
- Subgroup.comapstatement · cited by 154
- MonoidHom.range_eq_topproof · cited by 29
- Subgroup.map_comap_eq_selfproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- MulAction.IsBlock.translateproof · cited by 5
- QuotientGroup.ker_liftproof · cited by 3
- IsSimpleGroup.isSimpleGroup_of_surjectiveproof · cited by 1