Theorems · Theorem · nonassociative algebras

NonUnitalAlgebra.map_inf

∀ {F : Type u_1} {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] [inst_7 : IsScalarTower R A A] [inst_8 : SMulCommClass R A A]
  [inst_9 : IsScalarTower R B B] [inst_10 : SMulCommClass R B B] (f : F),
  Function.Injective ⇑f →
    ∀ (S T : NonUnitalSubalgebra R A),
      NonUnitalSubalgebra.map f (S ⊓ T) = NonUnitalSubalgebra.map f S ⊓ NonUnitalSubalgebra.map f T

Defined in

Mathlib.Algebra.Algebra.NonUnitalSubalgebra

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleNonUnitalNonAssocSemiringModuleFunLikeNonUnitalAlgHomClassIsScalarTowerSMulCommClassIsScalarTowerSMulCommClass