Theorems · Definition · commutative algebra

GradedRingHom.comp

{ι : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      {C : Type u_4} →
        {σ : Type u_6} →
          {τ : Type u_7} →
            {ψ : Type u_8} →
              [inst : Semiring A] →
                [inst_1 : Semiring B] →
                  [inst_2 : Semiring C] →
                    [inst_3 : SetLike σ A] →
                      [inst_4 : SetLike τ B] →
                        [inst_5 : SetLike ψ C] →
                          {𝒜 : ι → σ} → {ℬ : ι → τ} → {𝒞 : ι → ψ} → (ℬ →+*ᵍ 𝒞) → (𝒜 →+*ᵍ ℬ) → 𝒜 →+*ᵍ 𝒞

Composition of graded ring homomorphisms is a graded ring homomorphism.

Defined in

Mathlib.RingTheory.GradedAlgebra.RingHom

Cited by

18 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringSemiringSetLikeSetLikeSetLike