Theorems · Definition · convex and discrete geometry

PointedCone.map

{R : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : Semiring R] →
        [inst_1 : PartialOrder R] →
          [inst_2 : IsOrderedRing R] →
            [inst_3 : AddCommMonoid E] →
              [inst_4 : Module R E] →
                [inst_5 : AddCommMonoid F] → [inst_6 : Module R F] → (E →ₗ[R] F) → PointedCone R E → PointedCone R F

The image of a pointed cone under an R-linear map is a pointed cone.

Defined in

Mathlib.Geometry.Convex.Cone.Pointed

Cited by

19 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsOrderedRingAddCommMonoidModuleAddCommMonoidModule