Theorems · Theorem · ring theory

GradedAlgHom.restrictScalars_coe_algHom

Deprecated since 2026-05-05Use GradedAlgHom.restrictScalars_toAlgHom instead.

∀ {R : Type u_1} {A : Type u_6} {B : Type u_7} {ι : Type u_10} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Semiring B] [inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : DecidableEq ι] [inst_6 : AddMonoid ι]
  {𝒜 : ι → Submodule R A} {ℬ : ι → Submodule R B} [inst_7 : GradedAlgebra 𝒜] [inst_8 : GradedAlgebra ℬ] (R₀ : Type u_11)
  [inst_9 : CommSemiring R₀] [inst_10 : Algebra R₀ R] [inst_11 : Algebra R₀ A] [inst_12 : Algebra R₀ B]
  [inst_13 : IsScalarTower R₀ R A] [inst_14 : IsScalarTower R₀ R B] (f : 𝒜 →ₐᵍ[R] ℬ),
  AlgHom.restrictScalars R₀ ↑f = ↑(↑R₀ f)

Alias of GradedAlgHom.restrictScalars_toAlgHom.

Defined in

Mathlib.RingTheory.GradedAlgebra.AlgHom

Cited by

0 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraDecidableEqAddMonoidGradedAlgebraGradedAlgebraCommSemiringAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower