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Theorems · Theorem · ring theory

MonoidAlgebra.coeff_tensorEquiv_apply

∀ (R : Type u_1) {M : Type u_2} {N : Type u_3} [inst : CommSemiring R]
  (x : TensorProduct R (MonoidAlgebra R M) (MonoidAlgebra R N)),
  ((MonoidAlgebra.tensorEquiv R) x).coeff =
    (finsuppTensorFinsupp' R M N)
      ((TensorProduct.congr (MonoidAlgebra.coeffLinearEquiv R) (MonoidAlgebra.coeffLinearEquiv R)) x)
Defined in
Mathlib.RingTheory.TensorProduct.MonoidAlgebra
Cited by
2 results in Mathlib
Foundations
Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiring
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Around this declaration

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MonoidAlgebra.tensorEquiv_single_tmul_single · cited by 8MonoidAlgebra.tensorEquiv…Representation.LinearizeMonoidal.coeff_μ_tmul · cited by 0LinearizeMonoidal.coeff_μ…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idCommSemiring · cited by 10911CommSemiringFinsupp · cited by 5255FinsuppLinearEquiv · cited by 3317LinearEquivTensorProduct · cited by 2545TensorProductMonoidAlgebra · cited by 590MonoidAlgebraMonoidAlgebra.coeff · cited by 224MonoidAlgebra.coeffTensorProduct.congr · cited by 50TensorProduct.congrMonoidAlgebra.coeffLinearEquiv · cited by 34MonoidAlgebra.coeffLinear…finsuppTensorFinsupp' · cited by 24finsuppTensorFinsupp'MonoidAlgebra.tensorEquiv · cited by 14MonoidAlgebra.tensorEquivMonoidAlgebra.coeff_tensorEqu…CITED BYCITES

Cites12

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Cited by2

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