Mathlib Map

Theorems · Definition · group theory

smulMonoidWithZeroHom

{M₀ : Type u_5} →
  {N₀ : Type u_6} →
    [inst : MonoidWithZero M₀] →
      [inst_1 : MulZeroOneClass N₀] →
        [inst_2 : MulActionWithZero M₀ N₀] → [IsScalarTower M₀ N₀ N₀] → [SMulCommClass M₀ N₀ N₀] → M₀ × N₀ →*₀ N₀

Scalar multiplication as a monoid homomorphism with zero.

Defined in
Mathlib.Algebra.GroupWithZero.Action.Basic
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
MonoidWithZeroMulZeroOneClassMulActionWithZeroIsScalarTowerSMulCommClass

Around this declaration

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

Cites10

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

Cited by1

Results whose statement or proof uses this declaration.