Theorems · Theorem · group theory
AddMonoidHom.ker_eq_bot
∀ {G : Type u_1} [inst : AddGroup G] {M : Type u_7} [inst_1 : AddZeroClass M] (f : G →+ M),
Function.Injective ⇑f → f.ker = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddZeroClass
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
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- AddMonoidHom.kerstatement · cited by 158
- AddMonoidHom.ker_eq_bot_iffproof · cited by 14
Cited by7
Results whose statement or proof uses this declaration.
- AddSubgroup.comap_map_eq_self_of_injectiveproof · cited by 5
- AddSubgroup.index_map_of_bijectiveproof · cited by 2
- AddMonoidHom.ker_comp_of_injectiveproof · cited by 1
- AddSubgroup.index_map_of_injectiveproof · cited by 1
- AddSubgroup.ker_inclusionproof · cited by 0
- AddSubgroup.map_eq_bot_iff_of_injectiveproof · cited by 0
- AddSubgroup.ker_subtypeproof · cited by 0