Remark
Tag 061S, permanent. Cite it as [Bourbaki, Tag 061S].
Algebra, chapter III, § 5. Tensor algebra. Tensors
The above results can equally be obtained as a consequence of the universal properties of the free associative algebra of the tensor algebra, using II, § 3, no. 7, Corollary 2 to Proposition 7.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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