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Theorems · Definition · group theory

FunLike.commSemigroup

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

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

Defined in
Mathlib.Data.FunLike.Group
Cited by
0 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext, Quot.sound
Assumes
FunLikeMulCommSemigroupIsMulApply
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DFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeCommSemigroup · cited by 62CommSemigroupIsMulApply · cited by 18IsMulApplyFunction.Injective.commSemigroup · cited by 0Injective.commSemigroupFunLike.commSemigroupCITED BYCITES

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