Theorems · Theorem · group theory
AddMonoidHom.range_eq_top_of_surjective
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_7} [inst_1 : AddGroup N] (f : G →+ N),
Function.Surjective ⇑f → f.range = ⊤The range of a surjective AddMonoid homomorphism is the whole of the codomain.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 5 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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidHom.rangestatement · cited by 142
- AddMonoidHom.range_eq_topproof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- AddSubgroup.Normal.mapproof · cited by 3
- AddGroup.nilpotent_of_surjectiveproof · cited by 2
- AddGroup.nilpotencyClass_le_of_surjectiveproof · cited by 1
- AddSubgroup.index_map_dvdproof · cited by 1
- AddSubgroup.comap_eq_ker_of_surjectiveproof · cited by 0