Theorems · Definition · group theory
AddMonoidHom.range
{G : Type u_1} → [inst : AddGroup G] → {N : Type u_5} → [inst_1 : AddGroup N] → (G →+ N) → AddSubgroup NThe range of an AddMonoidHom from an AddGroup is an AddSubgroup.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 142 results in Mathlib
- Foundations
- Depth 22 from the axioms, rests on 165 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Top.topproof · cited by 9,680
- Set.rangeproof · cited by 4,705
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddSubgroup.mapproof · cited by 189
- AddSubgroup.copyproof · cited by 2
Cited by170
Results whose statement or proof uses this declaration.
- AddMonoidHom.range_eq_topstatement · cited by 20
- AddMonoidHom.mem_rangestatement · cited by 16
- AddSubgroup.range_subtypestatement and proof · cited by 16
- AddMonoidHom.range_eq_mapstatement · cited by 15
- AddMonoidHom.rangeRestrictstatement and proof · cited by 14
- NormedAddGroupHom.rangeproof · cited by 11
- MeasureTheory.Lp.boundedContinuousFunctionproof · cited by 7
- CategoryTheory.ShortComplex.abLeftHomologyDataproof · cited by 7
- AddSubgroup.map_comap_eqstatement and proof · cited by 5
- AddMonoidHom.map_rangestatement and proof · cited by 5
- AddMonoidHom.range_eq_top_of_surjectivestatement · cited by 5
- AddGroupExtension.range_inl_eq_ker_rightHomstatement · cited by 5