Theorems · Theorem · ring theory

GradedRing.proj_recompose

∀ {ι : Type u_1} {A : Type u_3} {σ : Type u_4} [inst : DecidableEq ι] [inst_1 : AddMonoid ι] [inst_2 : Semiring A]
  [inst_3 : SetLike σ A] [inst_4 : AddSubmonoidClass σ A] (𝒜 : ι → σ) [inst_5 : GradedRing 𝒜]
  (a : DirectSum ι fun i => ↥(𝒜 i)) (i : ι),
  (GradedRing.proj 𝒜 i) ((DirectSum.decompose 𝒜).symm a) =
    (DirectSum.decompose 𝒜).symm ((DirectSum.of (fun i => ↥(𝒜 i)) i) (a i))

Defined in

Mathlib.RingTheory.GradedAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddMonoidSemiringSetLikeAddSubmonoidClassGradedRing