Theorems · Theorem · commutative algebra
LinearMap.lTensor_smul
∀ {R : Type u_1} [inst : CommSemiring R] (M : Type u_7) {N : Type u_8} {P : Type u_9} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : Module R M] [inst_5 : Module R N]
[inst_6 : Module R P] (r : R) (f : N →ₗ[R] P), LinearMap.lTensor M (r • f) = r • LinearMap.lTensor M f- Defined in
- Mathlib.LinearAlgebra.TensorProduct.Map
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- LinearMap.lTensorstatement · cited by 203
- LinearMap.map_smulproof · cited by 60
- LinearMap.lTensorHomproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.lTensor_smul_actionproof · cited by 1
- ContinuousLinearMap.lTensor_smulproof · cited by 0