Theorems · Theorem · group theory
AddMonoidHom.eq_iff
∀ {G : Type u_1} [inst : AddGroup G] {M : Type u_7} [inst_1 : AddZeroClass M] (f : G →+ M) {x y : G},
f x = f y ↔ -y + x ∈ f.ker- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- AddGroupAddZeroClass
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- map_zeroproof · cited by 1,614
- AddZeroClassstatement and proof · cited by 1,237
- map_addproof · cited by 964
- add_assocproof · cited by 746
- neg_add_cancelproof · cited by 256
- add_neg_cancelproof · cited by 213
Cited by2
Results whose statement or proof uses this declaration.
- AddMonoidHom.ker_eq_bot_iffproof · cited by 14
- QuotientAddGroup.con_ker_eq_addConKerproof · cited by 0