Theorems · Definition · group theory
PresentedMonoid
{α : Type u_1} → (FreeMonoid α → FreeMonoid α → Prop) → Type u_1Given a set of relations, rels, over a type α, PresentedMonoid constructs the monoid with
generators x : α and relations rels as a quotient of a congruence structure over rels.
- Defined in
- Mathlib.Algebra.PresentedMonoid.Basic
- Cited by
- 10 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FreeMonoidstatement and proof · cited by 147
- Con.Quotientproof · cited by 48
- conGenproof · cited by 23
Cited by13
Results whose statement or proof uses this declaration.
- PresentedMonoid.mkstatement · cited by 7
- PresentedMonoid.ofstatement · cited by 5
- PresentedMonoid.inductionOnstatement and proof · cited by 2
- PresentedMonoid.liftstatement · cited by 2
- PresentedMonoid.closure_range_ofstatement and proof · cited by 1
- PresentedMonoid.extstatement and proof · cited by 1
- PresentedMonoid.mk_eq_mk_iffstatement · cited by 1
- PresentedMonoid.ext_iffstatement and proof · cited by 0
- PresentedMonoid.inductionOn₂statement and proof · cited by 0
- PresentedMonoid.inductionOn₃statement and proof · cited by 0
- PresentedMonoid.lift_ofstatement · cited by 0
- PresentedMonoid.mk_eq_mk_of_relstatement · cited by 0