Theorems · Definition · nonassociative algebras

NonUnitalAlgHom.codRestrict

{F : Type v'} →
  {R : Type u} →
    {A : Type v} →
      {B : Type w} →
        [inst : CommSemiring R] →
          [inst_1 : NonUnitalNonAssocSemiring A] →
            [inst_2 : Module R A] →
              [inst_3 : NonUnitalNonAssocSemiring B] →
                [inst_4 : Module R B] →
                  [inst_5 : FunLike F A B] →
                    [NonUnitalAlgHomClass F R A B] →
                      (f : F) → (S : NonUnitalSubalgebra R B) → (∀ (x : A), f x ∈ S) → A →ₙₐ[R] ↥S

Restrict the codomain of a non-unital algebra homomorphism.

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

3 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleNonUnitalNonAssocSemiringModuleFunLikeNonUnitalAlgHomClass