Theorems · Theorem · linear algebra
dualTensorHom_bijective
∀ {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] [Module.Finite R M] [Module.Projective R M],
Function.Bijective ⇑(dualTensorHom R M N)- Defined in
- Mathlib.LinearAlgebra.Contraction
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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 and proof · cited by 2,545
- LinearMap.compproof · cited by 1,642
- Module.Finitestatement and proof · cited by 1,032
- Function.Bijectivestatement · cited by 863
- LinearMap.extproof · cited by 844
- LinearMap.idproof · cited by 625
Cited by7
Results whose statement or proof uses this declaration.
- dualTensorHomEquivproof · cited by 9
- LinearMap.trace_transposeproof · cited by 1
- rTensorHomEquivHomRTensor_toLinearMapproof · cited by 1
- Module.Free.bijective_algebraMap_of_finrank_eq_oneproof · cited by 1
- lTensorHomEquivHomLTensor_toLinearMapproof · cited by 1
- LinearMap.trace_prodMapproof · cited by 1
- Representation.Equiv.dualTensorHom_invFunstatement · cited by 0