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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 8th 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded a reference * [[Jacob Lurie]], _Ultracategories_, ([pdf](http://www.math.harvard.edu/~lurie/papers/Conceptual.pdf)) <a href="https://ncatlab.org/nlab/revision/diff/ultracategory/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/ultracategory/4">v4</a>, <a href="https://ncatlab.org/nlab/show/ultracategory">current</a>

   Added a reference

   • Jacob Lurie, Ultracategories, (pdf)

   diff, v4, current

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeApr 14th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexDoes anything prevent a [[codensity monad]] construction for the inclusion of [[FinCat]] into [[Cat]]?

   Does anything prevent a codensity monad construction for the inclusion of FinCat into Cat?

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeApr 14th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexMike's asking about the inclusion of finitely presented $\infty$-groupoids, back [here](https://golem.ph.utexas.edu/category/2012/09/where_do_ultrafilters_come_fro.html#c044283). Does changing 'finite' to 'finitely presented' make a difference to my question?

   Mike’s asking about the inclusion of finitely presented $\infty$-groupoids, back here. Does changing ’finite’ to ’finitely presented’ make a difference to my question?

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeApr 14th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI guess there’s also the inclusion of finite sets into $Cat$ as discrete categories. That might be nearer ultracategories.

   I guess there’s also the inclusion of finite sets into $Cat$ as discrete categories. That might be nearer ultracategories.

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeApr 16th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded a reference * [[Francisco Marmolejo]], _Ultraproducts and continuous families of models_, ([thesis](https://dalspace.library.dal.ca/handle/10222/55092), poor quality photocopy). <a href="https://ncatlab.org/nlab/revision/diff/ultracategory/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/ultracategory/5">v5</a>, <a href="https://ncatlab.org/nlab/show/ultracategory">current</a>

   Added a reference

   • Francisco Marmolejo, Ultraproducts and continuous families of models, (thesis, poor quality photocopy).

   diff, v5, current

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 23rd 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI was thinking ultracategories should be a kind of [[generalized multicategory]], and it seems they (or least some form of them) are. * [[Maria Manuel Clementino]], [[Walter Tholen]], _Metric, topology and multicategory--a common approach_, J. Pure Appl. Algebra 179 (2003) 13-47, ([doi:10.1016/S0022-4049(02)00246-3](https://doi.org/10.1016/S0022-4049%2802%2900246-3)). I don't know why they say > we introduce a new structure called ultracategory which simultaneously generalizes the notions of topological space and of category when Makkai had already coined the term. Seeing that Lurie's notion is slightly different from the latter's, there's then the question of where this third notion fits. <a href="https://ncatlab.org/nlab/revision/diff/ultracategory/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/ultracategory/7">v7</a>, <a href="https://ncatlab.org/nlab/show/ultracategory">current</a>

   I was thinking ultracategories should be a kind of generalized multicategory, and it seems they (or least some form of them) are.

   • Maria Manuel Clementino, Walter Tholen, Metric, topology and multicategory–a common approach, J. Pure Appl. Algebra 179 (2003) 13-47, (doi:10.1016/S0022-4049(02)00246-3).

   I don’t know why they say

   we introduce a new structure called ultracategory which simultaneously generalizes the notions of topological space and of category

   when Makkai had already coined the term. Seeing that Lurie’s notion is slightly different from the latter’s, there’s then the question of where this third notion fits.

   diff, v7, current

7. • CommentRowNumber7.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 23rd 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded a little more detail. Also that the Clementino-Tholen concept is different. <a href="https://ncatlab.org/nlab/revision/diff/ultracategory/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/ultracategory/8">v8</a>, <a href="https://ncatlab.org/nlab/show/ultracategory">current</a>

   Added a little more detail. Also that the Clementino-Tholen concept is different.

   diff, v8, current

8. • CommentRowNumber8.
   • CommentAuthornLab edit announcer
   • CommentTimeOct 28th 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexchanged Marmolejo thesis link to better-quality scan Peter LeFanu Lumsdaine <a href="https://ncatlab.org/nlab/revision/diff/ultracategory/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/ultracategory/12">v12</a>, <a href="https://ncatlab.org/nlab/show/ultracategory">current</a>

   changed Marmolejo thesis link to better-quality scan

   Peter LeFanu Lumsdaine

   diff, v12, current