Timeline for Categories of finite objects
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 20, 2015 at 16:12 | answer | added | Manuel Bärenz | timeline score: -1 | |
| Aug 10, 2015 at 19:50 | comment | added | SorcererofDM | @QiaochuYuan that's part of the question, whether this finitude is a red herring. | |
| Aug 10, 2015 at 18:36 | comment | added | Todd Trimble | On the other hand, why there hasn't been more interaction between category theory and say graph theory (the kind that might appeal to Erdos) is IMO a rather interesting question. The Robertson-Seymour theorem on graph minors being quasi-well-ordered is an intensely interesting structural result that I would love to see category theorists pay attention to. | |
| Aug 10, 2015 at 17:35 | comment | added | Qiaochu Yuan | I don't really understand the question. You might be claiming that category theory doesn't say much about finite graphs, to be concrete, that combinatorialists might care about, but I think category theory doesn't say much about infinite graphs that combinatorialists might care about either. I think finitude is a red herring here and that your question is about something else. | |
| Aug 10, 2015 at 16:12 | comment | added | Zhen Lin | @TomBachmann Compact objects in the (∞, 1)-category of spaces are more general than finite CW complexes, however. | |
| Aug 10, 2015 at 15:39 | comment | added | SorcererofDM | What I had in mind was along the lines of 1) the typical objects that combinatorists work with (graphs, matroids, etc) and typical areas of interest exemplified by Szemerédi's theorem or graph minor theorem, or 2) data structures and things like circuits in CS (relatedly, finite model theory and descriptive complexity). | |
| Aug 10, 2015 at 14:54 | review | Close votes | |||
| Aug 13, 2015 at 2:31 | |||||
| Aug 10, 2015 at 14:38 | comment | added | Fernando Muro | Could you give a precise definition of what you mean when you speak about finite objects in a category? | |
| Aug 10, 2015 at 13:43 | comment | added | Tom Bachmann | It may (or may not) be helpful to note that "small" (finite?) objects are often characterised by being compact in their category. E.g. a compact $k$-vector space is the same as a finite-dimensional space, or (at the other end of the range of concreteness) a compact object in the stable homotopy category is the same as the natural generalisation of a finite CW complex. This way of embedding small (finite) objects into categories of huge objects is actually very useful, c/f Brown representability. | |
| Aug 10, 2015 at 12:50 | comment | added | David Roberts♦ | Fraïssé limits should be mentioned, I guess golem.ph.utexas.edu/category/2009/11/fraisse_limits.html | |
| Aug 10, 2015 at 12:35 | answer | added | Todd Trimble | timeline score: 6 | |
| Aug 10, 2015 at 12:29 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Aug 10, 2015 at 12:16 | history | asked | SorcererofDM | CC BY-SA 3.0 |