Theorems · Definition · ring theory

GradedAlgHom.mk.noConfusion

{R : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      {ι : Type u_4} →
        {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} →
                              {P : Sort u} →
                                {toAlgHom : A →ₐ[R] B} →
                                  {map_mem : ∀ {i : ι} {x : A}, x ∈ 𝒜 i → toAlgHom.toRingHom x ∈ ℬ i} →
                                    {toAlgHom' : A →ₐ[R] B} →
                                      {map_mem' : ∀ {i : ι} {x : A}, x ∈ 𝒜 i → toAlgHom'.toRingHom x ∈ ℬ i} →
                                        { toAlgHom := toAlgHom, map_mem := map_mem } =
                                            { toAlgHom := toAlgHom', map_mem := map_mem' } →
                                          (toAlgHom ≍ toAlgHom' → P) → P

Defined in

Mathlib.RingTheory.GradedAlgebra.AlgHom

Cited by

1 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound