codRestrict — Mathlib

English

The set-valued range of φ coincides with the set of values φ takes on A.

Русский

Множество значений φ совпадает с образом φ на A.

LaTeX

$$$\\operatorname{coeff}\\_{B}(\\mathrm{range}(\\phi)) = \\{ \\phi(a) : a \\in A \\}$$$

Lean4

/-- Restrict the codomain of a non-unital algebra homomorphism. -/
def codRestrict (f : F) (S : NonUnitalSubalgebra R B) (hf : ∀ x, f x ∈ S) : A →ₙₐ[R] S :=
  { NonUnitalRingHom.codRestrict (f : A →ₙ+* B) S.toNonUnitalSubsemiring hf with
    map_smul' := fun r a => Subtype.ext <| map_smul f r a }

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