Timeline for Naturally occurring examples of badly behaved categories
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2021 at 9:17 | comment | added | Martin Brandenburg | @TimCampion Good remark! So in a disjoint union for points $x,y$ in different spaces we let $d(x,y) = \infty$. (Which is just the general definition $\mathrm{Hom}(x,y)=0$ in a coproduct of enriched categories.) | |
| Apr 21, 2021 at 0:30 | comment | added | Tim Campion | Oh I see. You disallow infinite distances. Then my point is that if you "compactify" the category, by allowing distances to be infinite, you do get a complete and cocomplete category. | |
| Apr 20, 2021 at 23:24 | comment | added | Martin Brandenburg | @TimCampion My answer precisely refers to that category. non-increasing = metric (see the link). So I do not think that your statements are correct. | |
| Apr 20, 2021 at 22:51 | comment | added | Tim Campion | As with Andre's example, it's worth noting that if you restrict to the subcategory $Met_{\leq 1} \subset Met$ of distance non-increasing (i.e. 1-Lipschitz, or contractive maps), then you obtain a complete and cocomplete category which is generally well-behaved. | |
| S Apr 20, 2021 at 21:13 | history | answered | Martin Brandenburg | CC BY-SA 4.0 | |
| S Apr 20, 2021 at 21:13 | history | made wiki | Post Made Community Wiki by Martin Brandenburg |