powerAlgebraEquivFreeTensorAlgebra

English

The free product of a collection of R-algebras is defined as a quotient of the free tensor algebra by a freely generated relation.

Русский

Свободное произведение коллекции R-алгебр определяется как частное от свободной тензорной алгебры по свободной образующейся отношению.

LaTeX

$$$\\text{LinearAlgebra.FreeProduct} := \\text{RingQuot} (FreeProduct.rel R A)$$$

Lean4

/-- The free tensor algebra and its representation as an infinite direct sum
of tensor powers are (noncomputably) equivalent as `R`-algebras. -/
@[reducible]
noncomputable def powerAlgebraEquivFreeTensorAlgebra : PowerAlgebra R A ≃ₐ[R] FreeTensorAlgebra R A :=
  TensorAlgebra.equivDirectSum.symm

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