Theorems · Theorem · linear algebra

dualTensorHom_fun_bijective

∀ {ι : Type u_1} {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] [Finite ι],
  Function.Bijective ⇑(dualTensorHom R M N) → Function.Bijective ⇑(dualTensorHom R M (ι → N))

Defined in: Mathlib.LinearAlgebra.Contraction
Cited by: 1 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid AddCommMonoid Module Module Finite

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

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 · cited by 18,349
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement · cited by 10,215
Finitestatement and proof · cited by 3,029
TensorProductstatement · cited by 2,545
LinearEquiv.symmproof · cited by 1,461
LinearEquiv.toLinearMapproof · cited by 1,171
Function.Bijectivestatement and proof · cited by 863
LinearMap.extproof · cited by 844

Cited by1

Results whose statement or proof uses this declaration.

dualTensorHom_bijective_of_finite_projective_rightproof · cited by 0