Theorems · Definition · convex and discrete geometry

PointedCone.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] → PointedCone R G → PointedCone R H → PointedCone R (TensorProduct R G H)

The minimal tensor product of two cones is given by all conical combinations of elementary tensor products x ⊗ₜ y with x ∈ C₁ and y ∈ C₂.

Defined in

Mathlib.Geometry.Convex.Cone.TensorProduct

Cited by

8 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderIsStrictOrderedRingAddCommGroupModuleAddCommGroupModule