Theorems · Theorem · ring theory

GradedTensorProduct.lift_tmul

∀ {R : Type u_1} {ι : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring ι] [inst_1 : DecidableEq ι]
  [inst_2 : CommRing R] [inst_3 : Ring A] [inst_4 : Ring B] [inst_5 : Algebra R A] [inst_6 : Algebra R B]
  (𝒜 : ι → Submodule R A) (ℬ : ι → Submodule R B) [inst_7 : GradedAlgebra 𝒜] [inst_8 : GradedAlgebra ℬ]
  [inst_9 : Module ι (Additive ℤˣ)] {C : Type u_5} [inst_10 : Ring C] [inst_11 : Algebra R C] (f : A →ₐ[R] C)
  (g : B →ₐ[R] C)
  (h_anti_commutes : ∀ ⦃i j : ι⦄ (a : ↥(𝒜 i)) (b : ↥(ℬ j)), f ↑a * g ↑b = (-1) ^ (j * i) • (g ↑b * f ↑a)) (a : A)
  (b : B), (GradedTensorProduct.lift 𝒜 ℬ f g h_anti_commutes) (a ᵍ⊗ₜ[R] b) = f a * g b

Defined in

Mathlib.LinearAlgebra.TensorProduct.Graded.Internal

Cited by

2 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringDecidableEqCommRingRingRingAlgebraAlgebraGradedAlgebraGradedAlgebraModuleRingAlgebra