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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeApr 12th 2010
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI began writing the article [[club]], with more to come.

   I began writing the article club, with more to come.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeApr 12th 2010
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   Author: Mike Shulman
   Format: MarkdownItexThanks! I added some interspersed remarks about how clubs can be regarded as [[generalized operads]], and asked a question.

   Thanks! I added some interspersed remarks about how clubs can be regarded as generalized operads, and asked a question.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeApr 13th 2010
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   Author: Todd_Trimble
   Format: MarkdownItexThanks for those additions, Mike. I responded to your question, and will probably export my answer to the text when I get the chance.

   Thanks for those additions, Mike. I responded to your question, and will probably export my answer to the text when I get the chance.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeApr 14th 2016
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   Author: Mike Shulman
   Format: MarkdownItexI added a short section to [[club]] about the general notion of "club over a cartesian monad", with a reference. (I don't have at hand the correct references for the other versions; maybe some else can add them.) This is in preparation for hopefully generalizing it to cartesian monads *in* 2-categories other than $Cat$, including Garner's [double clubs](http://arxiv.org/abs/math/0606733). Has anyone seen other such generalizations of the notion of club?

   I added a short section to club about the general notion of “club over a cartesian monad”, with a reference. (I don’t have at hand the correct references for the other versions; maybe some else can add them.)

   This is in preparation for hopefully generalizing it to cartesian monads in 2-categories other than $Cat$, including Garner’s double clubs. Has anyone seen other such generalizations of the notion of club?

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeApr 20th 2017
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   Author: Mike Shulman
   Format: MarkdownItexI did some work on [[club]], mentioning the finite sets, many-objects, and over-Cat versions, and relating them all to polynomial monads. I am still rather puzzled by the mixed-variance case. I moved the parts of the query-box into the text that were not already there, except for a question and answer that I don't fully understand. If mixed-variance clubs are the generalized operads for some cartesian monad, what is that monad? It can't be polynomial. What are its algebras?

   I did some work on club, mentioning the finite sets, many-objects, and over-Cat versions, and relating them all to polynomial monads. I am still rather puzzled by the mixed-variance case. I moved the parts of the query-box into the text that were not already there, except for a question and answer that I don’t fully understand. If mixed-variance clubs are the generalized operads for some cartesian monad, what is that monad? It can’t be polynomial. What are its algebras?

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeOct 26th 2017
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   Author: Mike Shulman
   Format: MarkdownItexRe: #5, now I think maybe its algebras are strictly compact closed categories (i.e. symmetric strict monoidal categories equipped with a strictly involutive choice of duals) that are also enriched over pointed sets and such that all traces are the zero morphism. I can imagine it being cartesian. Is this version of the mixed-variance case, with the shape category enriched over pointed sets, in one of Kelly's papers? I can't find it right now.

   Re: #5, now I think maybe its algebras are strictly compact closed categories (i.e. symmetric strict monoidal categories equipped with a strictly involutive choice of duals) that are also enriched over pointed sets and such that all traces are the zero morphism. I can imagine it being cartesian.

   Is this version of the mixed-variance case, with the shape category enriched over pointed sets, in one of Kelly’s papers? I can’t find it right now.

7. • CommentRowNumber7.
   • CommentAuthormikestay
   • CommentTimeJan 9th 2019
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   Author: mikestay
   Format: TextWhat's the etymology of "club"? The social group or the weapon?

   What's the etymology of "club"? The social group or the weapon?
8. • CommentRowNumber8.
   • CommentAuthorMike Shulman
   • CommentTimeJan 9th 2019
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   Author: Mike Shulman
   Format: MarkdownItexBeats me. If I had to guess, I'd guess the social group, but it might be something entirely different.

   Beats me. If I had to guess, I’d guess the social group, but it might be something entirely different.

9. • CommentRowNumber9.
   • CommentAuthornLab edit announcer
   • CommentTimeJul 21st 2022
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   Author: nLab edit announcer
   Format: MarkdownItexremoving query box +--{: .query} [[Mike Shulman]]: Is this sort of club also a generalized operad for some cartesian monad on $Cat$? [[Todd Trimble]]: I'm pretty sure that it's a cartesian monad on $Cat$, and actually I don't know any real examples of Kelly's clubs which aren't. =-- Anonymous <a href="https://ncatlab.org/nlab/revision/diff/club/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/club/24">v24</a>, <a href="https://ncatlab.org/nlab/show/club">current</a>

   removing query box

   +–{: .query} Mike Shulman: Is this sort of club also a generalized operad for some cartesian monad on $Cat$?

   Todd Trimble: I’m pretty sure that it’s a cartesian monad on $Cat$, and actually I don’t know any real examples of Kelly’s clubs which aren’t. =–

   Anonymous

   diff, v24, current