Theorems · Theorem · nonassociative algebras

NonUnitalAlgHom.coe_distribMulActionHom_mk

∀ {R : Type u} {S : Type u₁} [inst : Monoid R] [inst_1 : Monoid S] {φ : R →* S} {A : Type v} {B : Type w}
  [inst_2 : NonUnitalNonAssocSemiring A] [inst_3 : DistribMulAction R A] [inst_4 : NonUnitalNonAssocSemiring B]
  [inst_5 : DistribMulAction S B] (f : A →ₛₙₐ[φ] B) (h₁ : ∀ (m : R) (x : A), f (m • x) = φ m • f x)
  (h₂ : { toFun := ⇑f, map_smul' := h₁ }.toFun 0 = 0)
  (h₃ :
    ∀ (x y : A),
      { toFun := ⇑f, map_smul' := h₁ }.toFun (x + y) =
        { toFun := ⇑f, map_smul' := h₁ }.toFun x + { toFun := ⇑f, map_smul' := h₁ }.toFun y)
  (h₄ :
    ∀ (x y : A),
      { toFun := ⇑f, map_smul' := h₁, map_zero' := h₂, map_add' := h₃ }.toFun (x * y) =
        { toFun := ⇑f, map_smul' := h₁, map_zero' := h₂, map_add' := h₃ }.toFun x *
          { toFun := ⇑f, map_smul' := h₁, map_zero' := h₂, map_add' := h₃ }.toFun y),
  ↑{ toFun := ⇑f, map_smul' := h₁, map_zero' := h₂, map_add' := h₃, map_mul' := h₄ } =
    { toFun := ⇑f, map_smul' := h₁, map_zero' := h₂, map_add' := h₃ }

Defined in

Mathlib.Algebra.Algebra.NonUnitalHom

Cited by

0 results in Mathlib

Foundations

Depth 20 from the axioms · uses no axioms

Assumes

MonoidMonoidNonUnitalNonAssocSemiringDistribMulActionNonUnitalNonAssocSemiringDistribMulAction