Theorems · Definition · commutative algebra

FunLike.distribMulAction

{M : Type u_1} →
  {F : Type u_3} →
    {α : Type u_4} →
      {β : Type u_5} →
        [i : FunLike F α β] →
          [inst : Monoid M] →
            [inst_1 : AddMonoid β] →
              [inst_2 : AddMonoid F] →
                [inst_3 : DistribMulAction M β] →
                  [inst_4 : SMul M F] →
                    [IsZeroApply F α β] → [IsAddApply F α β] → [IsSMulApply M F α β] → DistribMulAction M F

A FunLike type with scalar multiplication that satisfies (m • f) x = m • f x, 0 x = 0, (f + g) x = f x + g x is a DistribMulAction if β is a DistribMulAction.

Defined in

Mathlib.Data.FunLike.Module

Cited by

0 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

FunLikeMonoidAddMonoidAddMonoidDistribMulActionSMulIsZeroApplyIsAddApplyIsSMulApply