Timeline for Is the ultraproduct concept fundamentally category-theoretic?
Current License: CC BY-SA 4.0
16 events
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| S Jun 15, 2023 at 13:02 | history | suggested | The Amplitwist | CC BY-SA 4.0 |
replaced Unicode with MathJax (as per OP's comment below: https://mathoverflow.net/posts/comments/1158891)
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| Jun 15, 2023 at 12:21 | review | Suggested edits | |||
| S Jun 15, 2023 at 13:02 | |||||
| Jun 9, 2023 at 9:43 | comment | added | Joel David Hamkins | In case anyone is wondering, I had asked this question in the early days of MO, when the MathJax functionality was not working properly for me, and what I saw everywhere on MO was \full\blown\tex. So I had routinely used unicode characters at that time. If anyone wants to edit this to use proper formatting, please be my guest. | |
| Jun 9, 2023 at 9:03 | answer | added | varkor | timeline score: 5 | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jul 24, 2013 at 21:28 | answer | added | Joseph Van Name | timeline score: 5 | |
| Jul 11, 2013 at 5:10 | answer | added | Tom Leinster | timeline score: 45 | |
| Jul 6, 2010 at 16:50 | answer | added | Peter Arndt | timeline score: 8 | |
| Jul 6, 2010 at 15:02 | answer | added | Daniel Litt | timeline score: 9 | |
| May 28, 2010 at 16:55 | answer | added | Buschi Sergio | timeline score: 4 | |
| Jan 30, 2010 at 3:14 | answer | added | François G. Dorais | timeline score: 19 | |
| Jan 10, 2010 at 7:43 | answer | added | Andrej Bauer | timeline score: 8 | |
| Jan 9, 2010 at 23:35 | comment | added | François G. Dorais | Since I know there are several ways to do this, I really want a Category Theorist to answer and sort things out for us. Here is a summary of what I know, I will post details later if necessary. Ultraproducts are particular kinds of directed colimits, and it is often useful to describe them as such. Also, the ultraproduct $\prod_{i \in I} X_i/\mathcal{U}$ can be viewed as a stalk of a particular sheaf on $\beta I$. Anyway, I would really like to know more ways of thinking about ultraproducts in a categorical setting. I second this great question! | |
| Jan 9, 2010 at 23:31 | comment | added | Joel David Hamkins | Thanks for the link! Barr expresses the opinion there that ultraproducts are not defined by any universal mapping property. But I'm not really sure how one would prove such a thing. And will the category theorists really give up so easily? | |
| Jan 9, 2010 at 22:18 | comment | added | Qiaochu Yuan | I googled "ultraproduct universal property" and got this: dialinf.wordpress.com/2009/01/21/… . Apparently, the answer to your specific question about UMPs is "no." | |
| Jan 9, 2010 at 22:12 | history | asked | Joel David Hamkins | CC BY-SA 2.5 |