Theorems · Theorem · group theory
Subgroup.comap_eq_ker_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.comap f H = f.ker ↔ H = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 1 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.
Cites11
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
- Bot.botstatement and proof · cited by 4,720
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Disjointproof · cited by 2,201
- MonoidHom.kerstatement · cited by 212
- Subgroup.comapstatement · cited by 154
- MonoidHom.range_eq_top_of_surjectiveproof · cited by 7
- disjoint_topproof · cited by 5
- Subgroup.comap_eq_kerproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Group.IsPerfect.center_quotient_center_eq_botproof · cited by 0