Mathlib Map

Theorems · Definition · linear algebra

TensorProduct.rid

(R : Type u_1) →
  [inst : CommSemiring R] →
    (M : Type u_5) → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → TensorProduct R M R ≃ₗ[R] M

The base ring is a right identity for the tensor product of modules, up to linear equivalence.

Defined in
Mathlib.LinearAlgebra.TensorProduct.Associator
Cited by
63 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringAddCommMonoidModule

Around this declaration

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

TensorProduct.ridIsometry · cited by 9TensorProduct.ridIsometryRepresentation.TensorProduct.rid · cited by 7TensorProduct.ridAlgebra.TensorProduct.includeLeft_injective · cited by 5TensorProduct.includeLeft…QuadraticForm.tensorRId · cited by 5QuadraticForm.tensorRIdfinsuppTensorFinsuppRid · cited by 4finsuppTensorFinsuppRidModule.Invertible.rightCancelEquiv · cited by 4Invertible.rightCancelEqu…Algebra.TensorProduct.basisAux · cited by 3TensorProduct.basisAuxSemimoduleCat.MonoidalCategory.rightUnitor · cited by 3MonoidalCategory.rightUni…TensorProduct.rid_symm_apply · cited by 3TensorProduct.rid_symm_ap…TensorProduct.rid_tmul · cited by 3TensorProduct.rid_tmulAlgebra.TensorProduct.basisAux_tmul · cited by 2TensorProduct.basisAux_tm…Algebra.TensorProduct.basis_repr_symm_apply · cited by 2TensorProduct.basis_repr_…injective_lTensor_quotient_iff_inf_eq_mul · cited by 2injective_lTensor_quotien…TensorProduct.lid_eq_rid · cited by 2TensorProduct.lid_eq_ridfinsuppTensorFinsuppRid_single_tmul_single · cited by 1finsuppTensorFinsuppRid_s…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringLinearEquiv · cited by 3317LinearEquivTensorProduct · cited by 2545TensorProductLinearMap.flip · cited by 193LinearMap.flipTensorProduct.mk · cited by 129TensorProduct.mkTensorProduct.lift · cited by 59TensorProduct.liftLinearMap.lsmul · cited by 50LinearMap.lsmulLinearEquiv.ofLinearMap · cited by 9LinearEquiv.ofLinearMapTensorProduct.ridCITED BYCITES

Cites12

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

Cited by70

Results whose statement or proof uses this declaration.