Theorems · Definition · group theory
FreeSemigroup.toFreeMonoid
{α : Type u_1} → FreeSemigroup α →ₙ* FreeMonoid αThe natural embedding of the free semigroup into the free monoid.
This is injective (FreeSemigroup.toFreeMonoid_injective), and its image
consists of all non-1 elements of the free monoid (FreeSemigroup.eq_one_or_toFreeMonoid).
- Defined in
- Mathlib.Algebra.FreeMonoid.FreeSemigroup
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MulHomstatement · cited by 299
- FreeMonoidstatement · cited by 147
- FreeMonoid.ofproof · cited by 69
- FreeSemigroupstatement · cited by 43
- FreeSemigroup.liftproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- FreeMonoid.equivWithOneFreeSemigroupproof · cited by 2
- FreeSemigroup.toFreeMonoid_mk_eq_consstatement · cited by 1
- FreeSemigroup.eq_one_or_toFreeMonoidstatement and proof · cited by 0
- FreeSemigroup.range_toFreeMonoidstatement · cited by 0
- FreeSemigroup.toFreeMonoid_injectivestatement and proof · cited by 0
- FreeSemigroup.toFreeMonoid_ne_onestatement and proof · cited by 0
- FreeSemigroup.toFreeMonoid_ofstatement · cited by 0
- FreeMonoid.equivWithOneFreeSemigroup_symm_applystatement · cited by 0