Theorems · Theorem · group theory
MonoidHom.ker_eq_bot
∀ {G : Type u_1} [inst : Group G] {M : Type u_7} [inst_1 : MulOneClass M] (f : G →* M),
Function.Injective ⇑f → f.ker = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupMulOneClass
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.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- Bot.botstatement · cited by 4,720
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- MulOneClassstatement and proof · cited by 1,018
- MonoidHom.kerstatement · cited by 212
- MonoidHom.ker_eq_bot_iffproof · cited by 16
Cited by10
Results whose statement or proof uses this declaration.
- Subgroup.comap_map_eq_self_of_injectiveproof · cited by 7
- Group.isSolvable_of_isSolvable_injectiveproof · cited by 4
- IsPGroup.ker_isPGroup_of_injectiveproof · cited by 3
- MulAction.IsMultiplyPretransitive.index_of_fixingSubgroup_mulproof · cited by 2
- MonoidHom.ker_comp_of_injectiveproof · cited by 2
- Subgroup.index_map_of_bijectiveproof · cited by 1
- Subgroup.index_map_of_injectiveproof · cited by 1
- Subgroup.ker_inclusionproof · cited by 0
- Subgroup.map_eq_bot_iff_of_injectiveproof · cited by 0
- Subgroup.ker_subtypeproof · cited by 0