Mathlib Map

Theorems · Inductive type · group theory

Monoid

Type u → Type u

A Monoid is a Semigroup with an element 1 such that 1 * a = a * 1 = a.

Defined in
Mathlib.Algebra.Group.Defs
Cited by
3,887 results in Mathlib
Foundations
Depth 0 from the axioms, rests on 1 definitions · uses no axioms

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites0

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Nothing in Mathlib beyond the foundations.

Cited by5,078

Results whose statement or proof uses this declaration.

  • Unitsstatement · cited by 2,804
  • Units.valstatement and proof · cited by 1,966
  • IsUnitstatement and proof · cited by 1,602
  • one_smulstatement and proof · cited by 1,374
  • MulActionstatement · cited by 1,294
  • pow_zerostatement and proof · cited by 1,094
  • pow_onestatement and proof · cited by 894
  • Repstatement · cited by 843
  • Rep.Vstatement and proof · cited by 695
  • DistribMulActionstatement · cited by 584
  • one_powstatement and proof · cited by 521
  • map_powstatement and proof · cited by 503

Showing the 200 most cited of 5,078.