Theorems · Theorem · group theory
Subgroup.comap_map_eq
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] (f : G →* N) (H : Subgroup G),
Subgroup.comap f (Subgroup.map f H) = H ⊔ f.ker- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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_antisymmproof · cited by 2,068
- map_mulproof · cited by 1,137
- Subgroup.mapstatement and proof · cited by 301
- MonoidHom.kerstatement and proof · cited by 212
- sup_leproof · cited by 159
- Subgroup.comapstatement and proof · cited by 154
- inv_mul_cancelproof · cited by 107
- map_invproof · cited by 95
Cited by9
Results whose statement or proof uses this declaration.
- Subgroup.index_mapproof · cited by 6
- Subgroup.comap_map_eq_selfproof · cited by 4
- Subgroup.map_injective_of_ker_leproof · cited by 3
- MonoidHom.ker_transferSylow_isComplement'proof · cited by 3
- IsPGroup.to_sup_of_normal_rightproof · cited by 2
- Subgroup.IsFinitelyNormallyGenerated.comapproof · cited by 1
- Subgroup.relIndex_map_mapproof · cited by 0
- Subgroup.map_le_map_iffproof · cited by 0
- QuotientGroup.comap_map_mk'proof · cited by 0