Theorems · Theorem · ring theory
NonUnitalStarSubalgebra.map_map
∀ {R : Type u} {A : Type v} {B : Type w} {C : 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 : NonUnitalNonAssocSemiring C] [inst_8 : Module R C] [inst_9 : Star C] (S : NonUnitalStarSubalgebra R A)
(g : B →⋆ₙₐ[R] C) (f : A →⋆ₙₐ[R] B),
NonUnitalStarSubalgebra.map g (NonUnitalStarSubalgebra.map f S) = NonUnitalStarSubalgebra.map (g.comp f) S- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Starstatement and proof · cited by 496
- SetLike.coe_injectiveproof · cited by 374
- NonUnitalStarAlgHomstatement and proof · cited by 208
- NonUnitalStarSubalgebrastatement and proof · cited by 196
- Set.image_imageproof · cited by 140
- NonUnitalStarAlgHom.compstatement and proof · cited by 40
- NonUnitalStarSubalgebra.toNonUnitalSubalgebraproof · cited by 37
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.