Theorems · Theorem · ring theory

NonUnitalStarAlgHom.mk_coe

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : Monoid R] [inst_1 : NonUnitalNonAssocSemiring A]
  [inst_2 : DistribMulAction R A] [inst_3 : Star A] [inst_4 : NonUnitalNonAssocSemiring B]
  [inst_5 : DistribMulAction R B] [inst_6 : Star B] (f : A →⋆ₙₐ[R] B)
  (h₁ : ∀ (m : R) (x : A), f (m • x) = (MonoidHom.id R) 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)
  (h₅ :
    ∀ (a : A),
      { toFun := ⇑f, map_smul' := h₁, map_zero' := h₂, map_add' := h₃, map_mul' := h₄ }.toFun (star a) =
        star ({ toFun := ⇑f, map_smul' := h₁, map_zero' := h₂, map_add' := h₃, map_mul' := h₄ }.toFun a)),
  { toFun := ⇑f, map_smul' := h₁, map_zero' := h₂, map_add' := h₃, map_mul' := h₄, map_star' := h₅ } = f

Defined in

Mathlib.Algebra.Star.StarAlgHom

Cited by

0 results in Mathlib

Foundations

Depth 18 from the axioms · uses Quot.sound

Assumes

MonoidNonUnitalNonAssocSemiringDistribMulActionStarNonUnitalNonAssocSemiringDistribMulActionStar