Mathlib Map

Theorems · Definition · group theory

Matrix.SpecialLinearGroup.toPGL

{n : Type u_1} →
  {R : Type u_2} →
    [inst : Fintype n] →
      [inst_1 : DecidableEq n] → [inst_2 : CommRing R] → Matrix.SpecialLinearGroup n R →* Matrix.ProjGenLinGroup n R

The natural map from SL(n, R) to PGL(n, R) by composing the maps from SL to GL and the quotient map from GL to PGL.

Defined in
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Projective
Cited by
2 results in Mathlib
Foundations
Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeDecidableEqCommRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.ProjectiveSpecialLinearGroup.toPGL · cited by 4ProjectiveSpecialLinearGr…Matrix.SpecialLinearGroup.toPGL_ker · cited by 1SpecialLinearGroup.toPGL_…Matrix.ProjectiveSpecialLinearGroup.toPGL_injective · cited by 0ProjectiveSpecialLinearGr…CommRing · cited by 17173CommRingFintype · cited by 7736FintypeMonoidHom · cited by 3629MonoidHomMonoidHom.comp · cited by 469MonoidHom.compMatrix.SpecialLinearGroup · cited by 348Matrix.SpecialLinearGroupMatrix.SpecialLinearGroup.toGL · cited by 64SpecialLinearGroup.toGLMatrix.ProjGenLinGroup · cited by 23Matrix.ProjGenLinGroupMatrix.ProjGenLinGroup.mk · cited by 19ProjGenLinGroup.mkSpecialLinearGroup.toPGLCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.