Theorems · Theorem · linear algebra
dualTensorHom_comp_rTensor_dualMap
∀ {R : Type u_2} {M : Type u_3} {N : Type u_4} {P : Type u_5} [inst : CommSemiring R] [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] (f : M →ₗ[R] N),
dualTensorHom R M P ∘ₗ LinearMap.rTensor P f.dualMap = LinearMap.lcomp R P f ∘ₗ dualTensorHom R N P- Defined in
- Mathlib.LinearAlgebra.Contraction
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 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
- 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.compstatement and proof · cited by 1,642
- LinearMap.extproof · cited by 844
- Module.Dualstatement and proof · cited by 583
- LinearMap.rTensorstatement and proof · cited by 266
- TensorProduct.AlgebraTensorModule.curry_injectiveproof · cited by 159
Cited by1
Results whose statement or proof uses this declaration.
- dualTensorHom_bijectiveproof · cited by 6