Theorems · Definition · group theory
WithZero.lift
{α : Type u} → {β : Type v} → [inst : Add α] → [inst_1 : AddZeroClass β] → (α →ₙ+ β) ≃ (WithZero α →+ β)Lift an additive semigroup homomorphism f to a bundled additive monoid homomorphism.
- Defined in
- Mathlib.Algebra.Group.WithOne.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- AddAddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivstatement · cited by 8,337
- AddMonoidHomstatement and proof · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- WithZerostatement and proof · cited by 586
- AddHomstatement and proof · cited by 294
- AddHom.compproof · cited by 37
- WithZero.recZeroCoeproof · cited by 29
- AddMonoidHom.toAddHomproof · cited by 9
- WithZero.coeAddHomproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- WithZero.mapAddHomproof · cited by 9
- FreeAddMonoid.equivWithZeroFreeAddSemigroupproof · cited by 2
- WithZero.lift_coestatement · cited by 0
- WithZero.lift_symm_applystatement · cited by 0
- WithZero.lift_symm_injective_of_injectivestatement · cited by 0
- WithZero.lift_uniquestatement and proof · cited by 0
- WithZero.lift_zerostatement · cited by 0
- AddMonCat.adjoinZeroAdjproof · cited by 0
- FreeAddMonoid.equivWithZeroFreeAddSemigroup_symm_applystatement · cited by 0