Theorems · Definition · geometry

AffineEquiv.constVAdd

(k : Type u_1) →
  (P₁ : Type u_2) →
    {V₁ : Type u_6} →
      [inst : Ring k] →
        [inst_1 : AddCommGroup V₁] → [inst_2 : Module k V₁] → [inst_3 : AddTorsor V₁ P₁] → V₁ → P₁ ≃ᵃ[k] P₁

The map p ↦ v +ᵥ p as an affine automorphism of an affine space. Note that there is no need for an AffineMap.constVAdd as it is always an equivalence. This is roughly to DistribMulAction.toLinearEquiv as +ᵥ is to •.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineEquiv

Cited by

30 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor