Theorems · Definition · ring theory

NonUnitalStarAlgHom.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 : Star A] →
                [inst_4 : NonUnitalNonAssocSemiring B] →
                  [inst_5 : Module R B] →
                    [inst_6 : Star B] →
                      [inst_7 : FunLike F A B] →
                        [NonUnitalAlgHomClass F R A B] →
                          [StarHomClass F A B] →
                            (f : F) → (S : NonUnitalStarSubalgebra R B) → (∀ (x : A), f x ∈ S) → A →⋆ₙₐ[R] ↥S

Restrict the codomain of a non-unital star algebra homomorphism.

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

5 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleStarNonUnitalNonAssocSemiringModuleStarFunLikeNonUnitalAlgHomClassStarHomClass