Theorems · Theorem · algebraic geometry

HomogeneousLocalization.localRingHom.congr_simp

∀ {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] (f f_1 : 𝒜 →+*ᵍ ℬ) (e_f : f = f_1) (I : Ideal A)
  [inst_10 : I.IsPrime] (J : Ideal B) [inst_11 : J.IsPrime] (hIJ : I = Ideal.comap f J),
  HomogeneousLocalization.localRingHom f I J hIJ = HomogeneousLocalization.localRingHom f_1 I J ⋯

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Functor

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassAddCommMonoidDecidableEqGradedRingCommRingSetLikeAddSubgroupClassGradedRingIdeal.IsPrimeIdeal.IsPrime