Theorems · Theorem · ring theory

NonUnitalStarSubalgebra.map_le

∀ {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] [inst_8 : NonUnitalAlgHomClass F R A B] [inst_9 : StarHomClass F A B]
  {S : NonUnitalStarSubalgebra R A} {f : F} {U : NonUnitalStarSubalgebra R B},
  NonUnitalStarSubalgebra.map f S ≤ U ↔ S ≤ NonUnitalStarSubalgebra.comap f U

Defined in

Mathlib.Algebra.Star.NonUnitalSubalgebra

Cited by

2 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalNonAssocSemiringModuleStarNonUnitalNonAssocSemiringModuleStarFunLikeNonUnitalAlgHomClassStarHomClass