Theorems · Theorem · linear algebra

lTensorHomEquivHomLTensor_apply

∀ {R : Type u_2} {M : Type u_3} {P : Type u_5} {Q : Type u_6} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid P] [inst_3 : AddCommMonoid Q] [inst_4 : Module R M] [inst_5 : Module R P]
  [inst_6 : Module R Q] [inst_7 : Module.Projective R M] [inst_8 : Module.Finite R M]
  (x : TensorProduct R P (M →ₗ[R] Q)),
  (lTensorHomEquivHomLTensor R M P Q) x = (TensorProduct.lTensorHomToHomLTensor (RingHom.id R) M P Q) x

Defined in: Mathlib.LinearAlgebra.Contraction
Cited by: 1 results in Mathlib
Foundations: Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid AddCommMonoid AddCommMonoid Module Module Module Module.Projective Module.Finite

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Cites14

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
LinearEquivstatement · cited by 3,317
TensorProductstatement and proof · cited by 2,545
Module.Finitestatement and proof · cited by 1,032
Module.Projectivestatement and proof · cited by 82
LinearEquiv.coe_toLinearMapproof · cited by 15
lTensorHomEquivHomLTensorstatement and proof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

homTensorHomEquiv_toLinearMapproof · cited by 1