Theorems · Theorem · convex and discrete geometry

PointedCone.tmul_mem_minTensorProduct

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : LinearOrder R] [inst_2 : IsStrictOrderedRing R] {G : Type u_2}
  [inst_3 : AddCommGroup G] [inst_4 : Module R G] {H : Type u_3} [inst_5 : AddCommGroup H] [inst_6 : Module R H] {x : G}
  {y : H} {C₁ : PointedCone R G} {C₂ : PointedCone R H}, x ∈ C₁ → y ∈ C₂ → x ⊗ₜ[R] y ∈ C₁.minTensorProduct C₂

Elementary tensors are members of the minimal tensor product.

Defined in

Mathlib.Geometry.Convex.Cone.TensorProduct

Cited by

3 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderIsStrictOrderedRingAddCommGroupModuleAddCommGroupModule