Theorems · Definition · group theory
MonoidHom.rangeRestrict
{G : Type u_1} → [inst : Group G] → {N : Type u_5} → [inst_1 : Group N] → (f : G →* N) → G →* ↥f.rangeThe canonical surjective group homomorphism G →* f(G) induced by a group
homomorphism G →* N.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- MonoidHom.rangestatement and proof · cited by 314
- MonoidHom.codRestrictproof · cited by 8
Cited by19
Results whose statement or proof uses this declaration.
- MonoidHom.rangeRestrict_surjectivestatement and proof · cited by 6
- IsPGroup.mapproof · cited by 4
- surjective_of_isSwap_of_isPretransitive'proof · cited by 2
- MonoidHom.ofLeftInverseproof · cited by 2
- QuotientGroup.rangeKerLiftproof · cited by 2
- MonoidHom.ker_rangeRestrictstatement · cited by 1
- Function.MulExact.iff_monoidHom_rangeRestrictstatement · cited by 1
- Subgroup.card_range_dvdproof · cited by 1
- isZGroup_of_coprimeproof · cited by 1
- MonoidHom.isStrictMap_prodMap_iffproof · cited by 1
- MonoidHom.coe_rangeRestrictstatement · cited by 1
- MonoidHom.subtype_comp_rangeRestrictstatement · cited by 0