Theorems · Definition · geometry

AffineSubspace.gciMapComap

{k : Type u_1} →
  {V₁ : Type u_2} →
    {P₁ : Type u_3} →
      {V₂ : Type u_4} →
        {P₂ : Type u_5} →
          [inst : Ring k] →
            [inst_1 : AddCommGroup V₁] →
              [inst_2 : Module k V₁] →
                [inst_3 : AddTorsor V₁ P₁] →
                  [inst_4 : AddCommGroup V₂] →
                    [inst_5 : Module k V₂] →
                      [inst_6 : AddTorsor V₂ P₂] →
                        {f : P₁ →ᵃ[k] P₂} →
                          Function.Injective ⇑f → GaloisCoinsertion (AffineSubspace.map f) (AffineSubspace.comap f)

map f and comap f form a GaloisCoinsertion when f is injective.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorAddCommGroupModuleAddTorsor