Theorems · Definition · group theory
WithOne.lift
{α : Type u} → {β : Type v} → [inst : Mul α] → [inst_1 : MulOneClass β] → (α →ₙ* β) ≃ (WithOne α →* β)Lift a semigroup homomorphism f to a bundled 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
- MulMulOneClass
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
- MonoidHomstatement and proof · cited by 3,629
- MulOneClassstatement and proof · cited by 1,018
- MulHomstatement and proof · cited by 299
- WithOnestatement and proof · cited by 49
- MulHom.compproof · cited by 44
- MonoidHom.toMulHomproof · cited by 9
- WithOne.recOneCoeproof · cited by 8
- WithOne.coeMulHomproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- WithOne.mapMulHomproof · cited by 9
- FreeMonoid.equivWithOneFreeSemigroupproof · cited by 2
- MonCat.adjoinOneAdjproof · cited by 0
- WithOne.lift_coestatement · cited by 0
- WithOne.lift_onestatement · cited by 0
- WithOne.lift_symm_applystatement · cited by 0
- WithOne.lift_symm_injective_of_injectivestatement · cited by 0
- WithOne.lift_uniquestatement and proof · cited by 0
- FreeMonoid.equivWithOneFreeSemigroup_symm_applystatement · cited by 0