Theorems · Definition · group theory

FunLike.semigroup

{F : Type u_1} →
  {α : Type u_2} →
    {β : Type u_3} →
      [inst : FunLike F α β] → [inst_1 : Mul F] → [inst_2 : Semigroup β] → [IsMulApply F α β] → Semigroup F

A FunLike type that satisfies (f * g) x = f x * g x is a semigroup if β is a semigroup.

Defined in

Mathlib.Data.FunLike.Group

Cited by

0 results in Mathlib

Foundations

Depth 9 from the axioms · uses propext, Quot.sound

Assumes

FunLikeMulSemigroupIsMulApply