Theorems · Theorem · ring theory
TensorProduct.intrinsicStar_map
∀ {R : Type u_5} {E : Type u_6} {F : Type u_7} {G : Type u_8} {H : Type u_9} [inst : CommSemiring R]
[inst_1 : StarRing R] [inst_2 : AddCommMonoid E] [inst_3 : StarAddMonoid E] [inst_4 : Module R E]
[inst_5 : StarModule R E] [inst_6 : AddCommMonoid F] [inst_7 : StarAddMonoid F] [inst_8 : Module R F]
[inst_9 : StarModule R F] [inst_10 : AddCommMonoid G] [inst_11 : StarAddMonoid G] [inst_12 : Module R G]
[inst_13 : StarModule R G] [inst_14 : AddCommMonoid H] [inst_15 : StarAddMonoid H] [inst_16 : Module R H]
[inst_17 : StarModule R H] (f : WithConv (E →ₗ[R] F)) (g : WithConv (G →ₗ[R] H)),
star (WithConv.toConv (TensorProduct.map f.ofConv g.ofConv)) =
WithConv.toConv (TensorProduct.map (star f).ofConv (star g).ofConv)- Defined in
- Mathlib.Algebra.Star.LinearMap
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- TensorProductstatement · cited by 2,545
- StarRingstatement and proof · cited by 1,686
- TensorProduct.tmulproof · cited by 1,182
- Star.starstatement and proof · cited by 1,082
- StarModulestatement and proof · cited by 570
- StarAddMonoidstatement and proof · cited by 296
Cited by2
Results whose statement or proof uses this declaration.
- TensorProduct.star_map_apply_eq_map_intrinsicStarproof · cited by 1
- LinearMap.intrinsicStar_convMulproof · cited by 0