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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorJ-B Vienney
• CommentTimeJul 28th 2022

A few words and an hyperlink to a page where I will put my conjectural characterization of symmetric powers in symmetric monoidal categories enriched over modules over a $\mathbb{Q}^{+}$-algebra.

• CommentRowNumber2.
• CommentAuthorJ-B Vienney
• CommentTimeAug 13th 2022

Explained more generaly the construction of the symmetric algebra in a CMon-enriched symmetric monoidal category.

• CommentRowNumber3.
• CommentAuthorJ-B Vienney
• CommentTimeNov 19th 2022
• (edited Nov 19th 2022)

Added that permutations $\sigma:A^{\otimes n} \rightarrow A^{\otimes}$ are defined in the entry symmetric monoidal category

• CommentRowNumber4.
• CommentAuthorJ-B Vienney
• CommentTime7 days ago

Finally almost succeeded to prove this: symmetric powers in a symmetric monoidal $\mathbb{Q}^{+}$-linear category are characterized among the countable families of objects as forming a special connected graded quasi-bialgebra. Hope to add the reference soon.