Theorems · Theorem · commutative algebra

HomogeneousIdeal.comap_comap

∀ {A : Type u_1} {B : Type u_2} {C : Type u_3} {σ : Type u_4} {τ : Type u_5} {ω : Type u_6} {ι : Type u_7}
  [inst : Semiring A] [inst_1 : Semiring B] [inst_2 : Semiring C] [inst_3 : SetLike σ A] [inst_4 : SetLike τ B]
  [inst_5 : SetLike ω C] [inst_6 : AddSubmonoidClass σ A] [inst_7 : AddSubmonoidClass τ B]
  [inst_8 : AddSubmonoidClass ω C] [inst_9 : DecidableEq ι] [inst_10 : AddMonoid ι] {𝒜 : ι → σ} {ℬ : ι → τ} {𝒞 : ι → ω}
  [inst_11 : GradedRing 𝒜] [inst_12 : GradedRing ℬ] [inst_13 : GradedRing 𝒞] (f : 𝒜 →+*ᵍ ℬ) (g : ℬ →+*ᵍ 𝒞)
  {K : HomogeneousIdeal 𝒞}, HomogeneousIdeal.comap f (HomogeneousIdeal.comap g K) = HomogeneousIdeal.comap (g.comp f) K

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Maps

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringSemiringSetLikeSetLikeSetLikeAddSubmonoidClassAddSubmonoidClassAddSubmonoidClassDecidableEqAddMonoidGradedRingGradedRingGradedRing