Theorems · Theorem · nonassociative algebras

NonUnitalAlgHom.subtype_comp_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]
  [inst_6 : NonUnitalAlgHomClass F R A B] (f : F) (S : NonUnitalSubalgebra R B) (hf : ∀ (x : A), f x ∈ S),
  (NonUnitalSubalgebraClass.subtype S).comp (NonUnitalAlgHom.codRestrict f S hf) =
    NonUnitalAlgHomClass.toNonUnitalAlgHom f

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleNonUnitalNonAssocSemiringModuleFunLikeNonUnitalAlgHomClass