Theorems · Theorem · commutative algebra

DirectSum.decompose_map

∀ {ι : Type u_1} {A : Type u_2} {B : Type u_3} {σ : Type u_6} {τ : Type u_7} [inst : Semiring A] [inst_1 : Semiring B]
  [inst_2 : SetLike σ A] [inst_3 : SetLike τ B] [inst_4 : DecidableEq ι] [inst_5 : AddMonoid ι]
  [inst_6 : AddSubmonoidClass σ A] [inst_7 : AddSubmonoidClass τ B] (𝒜 : ι → σ) (ℬ : ι → τ) [inst_8 : GradedRing 𝒜]
  [inst_9 : GradedRing ℬ] {F : Type u_10} [inst_10 : FunLike F A B] [inst_11 : GradedFunLike F 𝒜 ℬ]
  [inst_12 : RingHomClass F A B] (f : F) {x : A},
  (DirectSum.decompose ℬ) (f x) = (DirectSum.map (↑f).gradedAddHom) ((DirectSum.decompose 𝒜) x)

Defined in

Mathlib.RingTheory.GradedAlgebra.RingHom

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringSetLikeSetLikeDecidableEqAddMonoidAddSubmonoidClassAddSubmonoidClassGradedRingGradedRingFunLikeGradedFunLikeRingHomClass