Theorems · Theorem · ring theory
StarSubalgebra.map_le_iff_le_comap
∀ {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : StarRing A] [inst_4 : Algebra R A] [inst_5 : StarModule R A] [inst_6 : Semiring B] [inst_7 : StarRing B]
[inst_8 : Algebra R B] [inst_9 : StarModule R B] {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {U : StarSubalgebra R B},
StarSubalgebra.map f S ≤ U ↔ S ≤ StarSubalgebra.comap f U- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- StarAlgHomstatement and proof · cited by 215
- Set.image_subset_iffproof · cited by 203
- StarSubalgebrastatement and proof · cited by 194
- StarSubalgebra.mapstatement · cited by 24
- StarSubalgebra.comapstatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- StarSubalgebra.gc_map_comapproof · cited by 2