Theorems · Definition · commutative algebra

FunLike.mulAction

{M : Type u_1} →
  {F : Type u_3} →
    {α : Type u_4} →
      {β : Type u_5} →
        [i : FunLike F α β] →
          [inst : SMul M F] → [inst_1 : Monoid M] → [inst_2 : MulAction M β] → [IsSMulApply M F α β] → MulAction M F

A FunLike type with scalar multiplication that satisfies (m • f) x = m • f x is a MulAction if β is a MulAction.

Defined in: Mathlib.Data.FunLike.Module
Cited by: 0 results in Mathlib
Foundations: Depth 10 from the axioms · uses propext, Quot.sound
Assumes: FunLike SMul Monoid MulAction IsSMulApply

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DFunLike.coeproof · cited by 62,936
Monoidstatement and proof · cited by 3,887
FunLikestatement and proof · cited by 2,560
MulActionstatement and proof · cited by 1,294
IsSMulApplystatement and proof · cited by 48
Function.Injective.mulActionproof · cited by 0

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