Theorems · Definition · ring theory
Algebra.TensorProduct.lid
(R : Type uR) → (A : Type uA) → [inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Algebra R A] → TensorProduct R R A ≃ₐ[R] A
The base ring is a left identity for the tensor product of algebra, up to algebra isomorphism.
- Defined in
- Mathlib.RingTheory.TensorProduct.Maps
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- TensorProductstatement · cited by 2,545
- AlgEquivstatement · cited by 1,681
- TensorProduct.lidproof · cited by 96
- Algebra.TensorProduct.algEquivOfLinearEquivTensorProductproof · cited by 1
Cited by16
Results whose statement or proof uses this declaration.
- Bialgebra.TensorProduct.lidproof · cited by 6
- Algebra.FormallyUnramified.isReduced_of_fieldproof · cited by 6
- Matrix.kroneckerAlgEquivproof · cited by 4
- Algebra.TensorProduct.lidOfCompatibleSMulproof · cited by 2
- IsAzumaya.tensorEquivEndproof · cited by 1
- Algebra.IsEffective.of_sectionproof · cited by 1
- Algebra.TensorProduct.lid_symm_applystatement · cited by 1
- Algebra.TensorProduct.lmul''_eq_lid_comp_mapOfCompatibleSMulstatement · cited by 0
- AlgCat.hom_hom_leftUnitorstatement · cited by 0
- Algebra.TensorProduct.lid_tmulstatement · cited by 0
- AlgCat.hom_inv_leftUnitorstatement · cited by 0
- Algebra.TensorProduct.lid_toLinearEquivstatement · cited by 0