Theorems · Theorem · geometry

Projectivization.map_injective

∀ {K : Type u_1} {V : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {L : Type u_3}
  {W : Type u_4} [inst_3 : DivisionRing L] [inst_4 : AddCommGroup W] [inst_5 : Module L W] {σ : K →+* L} {τ : L →+* K}
  [RingHomInvPair σ τ] (f : V →ₛₗ[σ] W) (hf : Function.Injective ⇑f), Function.Injective (Projectivization.map f hf)

Mapping with respect to a semilinear map over an isomorphism of fields yields an injective map on projective spaces.

Defined in

Mathlib.LinearAlgebra.Projectivization.Basic

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleDivisionRingAddCommGroupModuleRingHomInvPair