toFreeAbelianGroup — Mathlib

English

There is a canonical group homomorphism from X →₀ ℤ to FreeAbelianGroup X, given by a bilinear lifting construction.

Русский

Существует канонический гомоморфизм от X →₀ ℤ к FreeAbelianGroup X через лоиконструированное поднимание.

LaTeX

$$toFreeAbelianGroup : (X →₀ ℤ) →+ FreeAbelianGroup X$$

Lean4

/-- The group homomorphism `(X →₀ ℤ) →+ FreeAbelianGroup X`. -/
def toFreeAbelianGroup : (X →₀ ℤ) →+ FreeAbelianGroup X :=
  Finsupp.liftAddHom fun x => (smulAddHom ℤ (FreeAbelianGroup X)).flip (FreeAbelianGroup.of x)

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