Mathlib Map

Theorems · Definition · linear algebra

contractRight

(R : Type u_2) →
  (M : Type u_3) →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → TensorProduct R M (Module.Dual R M) →ₗ[R] R

The natural right-handed pairing between a module and its dual.

Defined in
Mathlib.LinearAlgebra.Contraction
Cited by
1 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringAddCommMonoidModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

contractRight_apply · cited by 0contractRight_applyModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringLinearMap · cited by 10215LinearMapTensorProduct · cited by 2545TensorProductLinearMap.id · cited by 625LinearMap.idModule.Dual · cited by 583Module.DualLinearMap.flip · cited by 193LinearMap.flipAddHom.toFun · cited by 168AddHom.toFunLinearMap.toAddHom · cited by 165LinearMap.toAddHomTensorProduct.uncurry · cited by 6TensorProduct.uncurrycontractRightCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.