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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeDec 30th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexCreated page, with definition. Berger-Mellies-Weber claim that the nerve theorem for monads with arities constructs Eilenberg-Moore and Kleisli objects in the 2-category of categories with arities, but as far as I can see their proof as written only shows that the Eilenberg-Moore adjunction lives in this 2-category, not that it retains its universal property there. Is there a quick way to see that it does? If this is true, then I think it gives an even *more* "natural" explanation of the nerve construction, along the lines of [Tom's original blog post](http://golem.ph.utexas.edu/category/2008/01/mark_weber_on_nerves_of_catego.html). <a href="https://ncatlab.org/nlab/revision/category+with+arities/1">v1</a>, <a href="https://ncatlab.org/nlab/show/category+with+arities">current</a>

   Created page, with definition.

   Berger-Mellies-Weber claim that the nerve theorem for monads with arities constructs Eilenberg-Moore and Kleisli objects in the 2-category of categories with arities, but as far as I can see their proof as written only shows that the Eilenberg-Moore adjunction lives in this 2-category, not that it retains its universal property there. Is there a quick way to see that it does? If this is true, then I think it gives an even more “natural” explanation of the nerve construction, along the lines of Tom’s original blog post.

   v1, current