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1. • CommentRowNumber1.
   • CommentAuthorJ-B Vienney
   • CommentTimeAug 9th 2022
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   Author: J-B Vienney
   Format: MarkdownItexI’ve thought that a R-linear category is a symmetric monoidal category enriched over $Mod_{R}$ but it seems to be just a category enriched over $Mod_{R}$. Is there a better name than symmetric monoidal category enriched over $Mod_{R}$ for this concept? I think tensor category is a little too vague and I need to precise the $R$.

   I’ve thought that a R-linear category is a symmetric monoidal category enriched over $Mod_{R}$ but it seems to be just a category enriched over $Mod_{R}$.

   Is there a better name than symmetric monoidal category enriched over $Mod_{R}$ for this concept? I think tensor category is a little too vague and I need to precise the $R$.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 9th 2022
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   Author: Urs
   Format: MarkdownItexMany authors say "[[tensor category]]" for monoidal $Vect$-enriched categories (possibly with further requirements, such as rigidity). So maybe a term like "symmetric $R$-tensor category" could serve your purpose.

   Many authors say “tensor category” for monoidal $Vect$-enriched categories (possibly with further requirements, such as rigidity).

   So maybe a term like “symmetric $R$-tensor category” could serve your purpose.