Theorems · Theorem · convex and discrete geometry

Convexity.IsAffineMap.map_iConvexComb

∀ {R : Type u_1} {M : Type u_3} {N : Type u_4} {I : Type u_6} [inst : PartialOrder R] [inst_1 : Semiring R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : Convexity.ConvexSpace R M] [inst_4 : Convexity.ConvexSpace R N]
  {f : M → N},
  Convexity.IsAffineMap R f →
    ∀ (s : Convexity.StdSimplex R I) (g : I → M), f (Convexity.iConvexComb s g) = Convexity.iConvexComb s (f ∘ g)

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

7 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpaceConvexity.ConvexSpace