Theorems · Theorem · group theory
AddMonoidHom.map_neg
∀ {α : Type u_2} {β : Type u_3} [inst : AddGroup α] [inst_1 : SubtractionMonoid β] (f : α →+ β) (a : α), f (-a) = -f aAdditive group homomorphisms preserve negation.
- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- AddGroupSubtractionMonoid
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.
- DFunLike.coestatement · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddMonoidHomstatement and proof · cited by 3,230
- map_negproof · cited by 378
- SubtractionMonoidstatement and proof · cited by 208
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.AddGrpObj.comp_negproof · cited by 9
- Finsupp.single_negproof · cited by 7
- CategoryTheory.Functor.map_negproof · cited by 7
- AddGroup.extproof · cited by 4
- Set.indicator_neg'proof · cited by 4
- Pi.single_negproof · cited by 3
- AddSubgroup.index_comap_of_surjectiveproof · cited by 2
- Circle.exp_negproof · cited by 1
- AddMonoidHom.liftOfRightInverseAux_comp_applyproof · cited by 1
- QuotientAddGroup.kerLift_injectiveproof · cited by 1
- Finsupp.erase_negproof · cited by 0
- FreeAbelianGroup.seq_negproof · cited by 0