Theorems · Theorem · ring theory
MonoidAlgebra.tensorEquiv_single_tmul_single
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommSemiring R] (m : M) (r₁ : R) (n : N) (r₂ : R),
(MonoidAlgebra.tensorEquiv R) (MonoidAlgebra.single m r₁ ⊗ₜ[R] MonoidAlgebra.single n r₂) =
MonoidAlgebra.single (m, n) (r₁ * r₂)- Cited by
- 8 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearEquivstatement · cited by 3,317
- TensorProductstatement · cited by 2,545
- TensorProduct.tmulstatement and proof · cited by 1,182
- Finsupp.singleproof · cited by 943
- MonoidAlgebrastatement · cited by 590
- Finsupp.extproof · cited by 399
- MonoidAlgebra.singlestatement and proof · cited by 253
- MonoidAlgebra.extproof · cited by 78
- finsuppTensorFinsupp'proof · cited by 24
Cited by8
Results whose statement or proof uses this declaration.
- Representation.LinearizeMonoidal.μ_apply_single_singleproof · cited by 1
- Representation.LinearizeMonoidal.δ_μproof · cited by 0
- Representation.LinearizeMonoidal.μ_comp_assocproof · cited by 0
- Representation.LinearizeMonoidal.μ_comp_lTensorproof · cited by 0
- Representation.LinearizeMonoidal.μ_comp_rTensorproof · cited by 0
- Representation.LinearizeMonoidal.μ_leftUnitorproof · cited by 0
- Representation.LinearizeMonoidal.μ_rightUnitorproof · cited by 0
- Representation.LinearizeMonoidal.μ_δproof · cited by 0