Timeline for Most harmful heuristic?
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Oct 27, 2018 at 9:37 | comment | added | Oscar Cunningham | I'd argue that categories really should be named after their objects, but that you can only tell what the objects really are by looking at the structure of the morphisms. For example the category $\mathbf{Rel}$ of "sets" and relations should really be called $\mathbf{FreeSupLat}$. | |
| Oct 27, 2018 at 5:12 | comment | added | Kapil | A version of this is trying to identify a group with its collection of irreducible representations or their characters. There is more in Tannaka duality. | |
| Nov 10, 2016 at 10:12 | comment | added | HeinrichD | @ToddTrimble: The category of metric spaces. There are 6 natural classes of morphisms which are also used in practice: continuous maps, short maps, isometric maps, Lipschitz maps, equicontinuous maps, quasi-isometries. | |
| Feb 14, 2015 at 3:47 | comment | added | Christopher King | Typically a category seems to be named after the objects unless there is already a category with the same objects unless (Set and Rel.) | |
| Sep 10, 2014 at 14:55 | comment | added | Manuel Bärenz | @PietroMajer, famous counterexample: The category of cobordisms. And maybe "Linear categories", if you wish. | |
| Apr 18, 2013 at 15:24 | comment | added | Todd Trimble | Ironically, I just had an example the other day (linear codes) where it wasn't completely clear to me what the correct notion of isomorphism should be!! So this is me answering my former (August 25 2012) self. | |
| Aug 25, 2012 at 19:40 | comment | added | Todd Trimble | I'd like to hear a convincing example where this has really been a problem. Usually there's a default notion of morphism (think of the category of sets, for instance), and in my experience, when anyone departs from the default, they make a point of it (e.g., the category or bicategory of sets and relations -- see, I didn't specify the 2-cells just now!). I hope Thierry can remember the details of his tale. | |
| Mar 13, 2011 at 15:24 | comment | added | Robert K | @Pietro With the exception of Ehresmann and his school. :-) | |
| Aug 18, 2010 at 22:02 | comment | added | Thierry Zell | It's worse! A classmate of mine once gave a talk about that very problem, where he explained how sloppiness with the very nature of the arrows had set back the understanding of a problem many years. I wish I could remember the topic, but it's been over 10 years. Still, even though I don't work with categories (explicitly), the essence of this chilling tale remains with me to this day. | |
| Jun 25, 2010 at 10:55 | comment | added | Pietro Majer | yet nobody is brave enough to name categories from the name of arrows, like if we said "category of continuous mapping" for Top, etc. | |
| Oct 24, 2009 at 22:03 | comment | added | Reid Barton | Similar abuses of language include naming a model category by its fibrant objects ("the model category of quasicategories") or a 2-category by its 1-morphisms ("the 2-category of spans"). | |
| Oct 24, 2009 at 21:49 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |