Theorems · Definition · group theory
PresentedMonoid.of
{α : Type u_1} → (rels : FreeMonoid α → FreeMonoid α → Prop) → α → PresentedMonoid relsof is the canonical map from α to a presented monoid with generators x : α. The term x
is mapped to the equivalence class of the image of x in FreeMonoid α.
- Defined in
- Mathlib.Algebra.PresentedMonoid.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Quot.sound
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.coeproof · cited by 62,936
- FreeMonoidstatement and proof · cited by 147
- FreeMonoid.ofproof · cited by 69
- PresentedMonoidstatement · cited by 10
- PresentedMonoid.mkproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- PresentedMonoid.closure_range_ofstatement and proof · cited by 1
- PresentedMonoid.extstatement and proof · cited by 1
- PresentedMonoid.ext_iffstatement and proof · cited by 0
- PresentedMonoid.lift_ofstatement · cited by 0
- PresentedMonoid.toMonoid.uniquestatement and proof · cited by 0