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1. • CommentRowNumber1.
   • CommentAuthorJames
   • CommentTimeAug 22nd 2020
   • (edited Aug 22nd 2020)
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   Author: James
   Format: MarkdownItexCould categories be considered generalized uniform structures, extending [[generalized uniform structures - table|this table]] by the following row? - proarrow -> directed graph - monad -> category - pro-monad -> ? - symmetric proarrow -> undirected graph - symmetric monad -> groupoid - symmetric pro-monad -> ?

   Could categories be considered generalized uniform structures, extending this table by the following row?

   • proarrow -> directed graph
   • monad -> category
   • pro-monad -> ?
   • symmetric proarrow -> undirected graph
   • symmetric monad -> groupoid
   • symmetric pro-monad -> ?
2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeAug 23rd 2020
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   Author: Mike Shulman
   Format: MarkdownItexCertainly there is such a row. I'm not sure I'd be inclined to consider a category to be a generalized uniform structure though, rather I would just say that both are an instance of a monad in a bicategory (or perhaps a bit more specifically a [[generalized multicategory]]). I'd forgotten the existence of this table. On which pages is it included?

   Certainly there is such a row. I’m not sure I’d be inclined to consider a category to be a generalized uniform structure though, rather I would just say that both are an instance of a monad in a bicategory (or perhaps a bit more specifically a generalized multicategory).

   I’d forgotten the existence of this table. On which pages is it included?

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeAug 23rd 2020
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   Author: TobyBartels
   Format: MarkdownItexIt\'s the pro-monads that are generalized uniform structures, not the monads themselves. Algebraic geometers seem to study pro-groupoids (which are to pro-groups as groupoids are to groups), but I haven\'t checked if that\'s really what goes in the last blank. If it does, then they are generalized uniform structures. The table is included in most of the pages that it links to, but not the ones for the simplest concepts.

   It's the pro-monads that are generalized uniform structures, not the monads themselves. Algebraic geometers seem to study pro-groupoids (which are to pro-groups as groupoids are to groups), but I haven't checked if that's really what goes in the last blank. If it does, then they are generalized uniform structures.

   The table is included in most of the pages that it links to, but not the ones for the simplest concepts.