Theorems · Theorem · group theory
MonoidHom.range_eq_top_of_surjective
∀ {G : Type u_1} [inst : Group G] {N : Type u_7} [inst_1 : Group N] (f : G →* N), Function.Surjective ⇑f → f.range = ⊤The range of a surjective monoid homomorphism is the whole of the codomain.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Top.topstatement · cited by 9,680
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- MonoidHom.rangestatement · cited by 314
- MonoidHom.range_eq_topproof · cited by 29
Cited by7
Results whose statement or proof uses this declaration.
- Subgroup.Normal.mapproof · cited by 4
- Group.isSolvable_of_surjectiveproof · cited by 4
- Group.nilpotent_of_surjectiveproof · cited by 3
- Subgroup.index_map_dvdproof · cited by 2
- Group.nilpotencyClass_le_of_surjectiveproof · cited by 2
- Subgroup.comap_eq_ker_of_surjectiveproof · cited by 1
- Group.IsPerfect.ofSurjectiveproof · cited by 0