Theorems · Theorem · group theory
Subgroup.comap_map_eq_self_of_injective
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N},
Function.Injective ⇑f → ∀ (H : Subgroup G), Subgroup.comap f (Subgroup.map f H) = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 73 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
- bot_leproof · cited by 306
- Subgroup.mapstatement · cited by 301
- Subgroup.comapstatement · cited by 154
- MonoidHom.ker_eq_botproof · cited by 10
- Subgroup.comap_map_eq_selfproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Subgroup.map_le_map_iff_of_injectiveproof · cited by 2
- Subgroup.relIndex_pointwise_smulproof · cited by 2
- Subgroup.map_injectiveproof · cited by 1
- Subgroup.Normal.of_map_injectiveproof · cited by 1
- Subgroup.relIndex_inter_ne_zeroproof · cited by 0
- Subgroup.relIndex_map_map_of_injectiveproof · cited by 0
- Subgroup.isArithmetic_iff_finiteIndexproof · cited by 0