Theorems · Theorem · group theory
MonoidHom.range_eq_top
∀ {G : Type u_1} [inst : Group G] {N : Type u_7} [inst_1 : Group N] {f : G →* N}, f.range = ⊤ ↔ Function.Surjective ⇑f- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Setproof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- MonoidHom.rangestatement · cited by 314
- SetLike.ext'_iffproof · cited by 78
- Set.range_eq_univproof · cited by 50
Cited by29
Results whose statement or proof uses this declaration.
- MonoidHom.range_eq_top_of_surjectiveproof · cited by 7
- MonoidHom.ker_transferSylow_isComplement'proof · cited by 3
- Subgroup.map_comap_eq_self_of_surjectiveproof · cited by 3
- zpowersHom_bijectiveproof · cited by 2
- surjective_of_isSwap_of_isPretransitive'proof · cited by 2
- MonoidHom.surjective_of_card_ker_le_divproof · cited by 2
- alternatingGroup.index_eq_twoproof · cited by 2
- FreeGroup.closure_range_ofproof · cited by 2
- Subgroup.comap_le_comap_of_surjectiveproof · cited by 2
- QuotientGroup.range_mk'proof · cited by 1
- Group.fg_iff_exists_freeGroup_hom_surjectiveproof · cited by 1
- CoxeterSystem.subgroup_closure_range_simpleproof · cited by 1