Theorems · Definition · ring theory

GradedAlgHom.ofClass

{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] →
                              {F : Type u_11} →
                                [inst_9 : FunLike F A B] →
                                  [GradedFunLike F 𝒜 ℬ] → [AlgHomClass F R A B] → F → 𝒜 →ₐᵍ[R] ℬ

Turn an element of a type F satisfying [FunLike F A B] [GradedFunLike F 𝒜 ℬ] [AlgHomClass F R A B] into an actual GradedAlgHom. In future mathlib this will be deprioritised in favour of using structural projections.

Defined in

Mathlib.RingTheory.GradedAlgebra.AlgHom

Cited by

3 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebraDecidableEqAddMonoidGradedAlgebraGradedAlgebraFunLikeGradedFunLikeAlgHomClass