Theorems · Definition · commutative algebra

HomogeneousLocalization.Away.map

{ι : Type u_1} →
  {A : Type u_2} →
    {σ : Type u_3} →
      [inst : CommRing A] →
        [inst_1 : SetLike σ A] →
          [inst_2 : AddSubgroupClass σ A] →
            [inst_3 : AddCommMonoid ι] →
              [inst_4 : DecidableEq ι] →
                {𝒜 : ι → σ} →
                  [inst_5 : GradedRing 𝒜] →
                    {B : Type u_4} →
                      {τ : Type u_5} →
                        [inst_6 : CommRing B] →
                          [inst_7 : SetLike τ B] →
                            [inst_8 : AddSubgroupClass τ B] →
                              {ℬ : ι → τ} →
                                [inst_9 : GradedRing ℬ] →
                                  (g : 𝒜 →+*ᵍ ℬ) →
                                    (f : A) → HomogeneousLocalization.Away 𝒜 f →+* HomogeneousLocalization.Away ℬ (g f)

If g : 𝒜 →+*ᵍ ℬ is a graded ring homomorphism and f : A then we have a map Away 𝒜 f →+* Away ℬ (g f).

Defined in

Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization

Cited by

10 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRingCommRingSetLikeAddSubgroupClassGradedRing