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1. • CommentRowNumber1.
   • CommentAuthorKarol Szumiło
   • CommentTimeAug 1st 2024
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   Author: Karol Szumiło
   Format: MarkdownItexThere was a fairly recent preprint on arXiv that I caught a quick glimpse of and now can't find again. It introduced some machinery for algebraic theories with restricted arities, perhaps introducing some operad-like notions. I remember that at least one notion concerned sets of arities $A \subseteq \mathbb{N}$ such that $a_1 + \ldots + a_k \in A$ whenever $k \in A$ and $a_1, \ldots, a_k \in A$. Can anyone recall which paper it was?

   There was a fairly recent preprint on arXiv that I caught a quick glimpse of and now can’t find again. It introduced some machinery for algebraic theories with restricted arities, perhaps introducing some operad-like notions. I remember that at least one notion concerned sets of arities $A \subseteq \mathbb{N}$ such that $a_1 + \ldots + a_k \in A$ whenever $k \in A$ and $a_1, \ldots, a_k \in A$. Can anyone recall which paper it was?

2. • CommentRowNumber2.
   • CommentAuthorJ-B Vienney
   • CommentTimeAug 2nd 2024
   • (edited Aug 2nd 2024)
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   Author: J-B Vienney
   Format: MarkdownItexMaybe you are thinking about my talk at FMCS 2024. I talk about the set of arities on slide 4. [slides](https://pages.cpsc.ucalgary.ca/~robin/FMCS/FMCS2024/slides/FMCS2024-Vienney.pdf). We talked quite a bit about this on Zulip. There is no preprint today because I thought that the notion wasn't yet enough general and is probably included into an existing notion. But maybe I should try to write one if there is some interest about this notion.

   Maybe you are thinking about my talk at FMCS 2024. I talk about the set of arities on slide 4. slides. We talked quite a bit about this on Zulip. There is no preprint today because I thought that the notion wasn’t yet enough general and is probably included into an existing notion. But maybe I should try to write one if there is some interest about this notion.

3. • CommentRowNumber3.
   • CommentAuthorJ-B Vienney
   • CommentTimeAug 2nd 2024
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   Author: J-B Vienney
   Format: MarkdownItexLet me know if this is not what you were thinking about. If there is a preprint as you said, then it is quite intriguing to me.

   Let me know if this is not what you were thinking about. If there is a preprint as you said, then it is quite intriguing to me.

4. • CommentRowNumber4.
   • CommentAuthorKarol Szumiło
   • CommentTimeAug 3rd 2024
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   Author: Karol Szumiło
   Format: MarkdownItexThe definition on your slide 4 is indeed the one that I was asking about. However, I haven't seen your talk and I'm pretty sure I haven't seen your slides until now either. I must have seen this notion in an arXiv paper not too long ago.

   The definition on your slide 4 is indeed the one that I was asking about. However, I haven’t seen your talk and I’m pretty sure I haven’t seen your slides until now either. I must have seen this notion in an arXiv paper not too long ago.