Mathlib Map

Theorems · Definition · geometry

AffineMap.homothetyHom

{k : Type u_2} →
  {V1 : Type u_3} →
    {P1 : Type u_4} →
      [inst : CommRing k] →
        [inst_1 : AddCommGroup V1] → [inst_2 : AddTorsor V1 P1] → [inst_3 : Module k V1] → P1 → k →* P1 →ᵃ[k] P1

homothety as a multiplicative monoid homomorphism.

Defined in
Mathlib.LinearAlgebra.AffineSpace.AffineMap
Cited by
2 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Quot.sound
Assumes
CommRingAddCommGroupAddTorsorModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AffineEquiv.homothetyUnitsMulHom · cited by 5AffineEquiv.homothetyUnit…AffineMap.coe_homothetyHom · cited by 0AffineMap.coe_homothetyHomAffineEquiv.coe_homothetyUnitsMulHom_eq_homothetyHom_coe · cited by 0AffineEquiv.coe_homothety…Module · cited by 20661ModuleCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupMonoidHom · cited by 3629MonoidHomAddTorsor · cited by 1657AddTorsorAffineMap · cited by 674AffineMapAffineMap.homothety · cited by 51AffineMap.homothetyAffineMap.homothety_one · cited by 3AffineMap.homothety_oneAffineMap.homothety_mul · cited by 0AffineMap.homothety_mulAffineMap.homothetyHomCITED BYCITES

Cites9

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.