map — Mathlib

English

A ring homomorphism f: R → S induces a group homomorphism from SL(n,R) to SL(n,S).

Русский

Кольцевой гомоморфизм f: R → S индуцирует groep-моморфизм из SL(n,R) в SL(n,S).

LaTeX

$$map (f : R →+* S) : SpecialLinearGroup n R →* SpecialLinearGroup n S$$

Lean4

/-- A ring homomorphism from `R` to `S` induces a group homomorphism from
`SpecialLinearGroup n R` to `SpecialLinearGroup n S`. -/
@[simps]
def map (f : R →+* S) : SpecialLinearGroup n R →* SpecialLinearGroup n S
    where
  toFun
    g :=
    ⟨f.mapMatrix ↑ₘg, by
      rw [← f.map_det]
      simp [g.prop]⟩
  map_one' := Subtype.ext <| f.mapMatrix.map_one
  map_mul' x y := Subtype.ext <| f.mapMatrix.map_mul ↑ₘx ↑ₘy

Похожие утверждения