Timeline for What are a couple of examples of finite sized but interesting categories?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2015 at 2:05 | answer | added | Noam D. Elkies | timeline score: 3 | |
| Jul 2, 2015 at 1:59 | comment | added | Kimball | More generally than Todd's finite group example, you can consider finite groupoids. For example, the ideal classes of a quaternion algebra form a finite groupoid (the Brandt groupoid). | |
| Jul 2, 2015 at 1:11 | answer | added | Andreas Blass | timeline score: 4 | |
| Jul 1, 2015 at 21:29 | review | Close votes | |||
| Jul 2, 2015 at 18:59 | |||||
| Jul 1, 2015 at 20:21 | comment | added | Eric Wofsey | For what it's worth, any finite category that has all finite products (or coproducts) is a preorder. | |
| Jul 1, 2015 at 18:38 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Jul 1, 2015 at 18:34 | comment | added | Benjamin Steinberg | If Q is a finite acyclic directed graph (called a quiver in this context) then the free category on Q (with vertex set the same as Q and arrows directed paths) is an interesting finite category. Functors from this category into the category of vector spaces is the same things as a quiver representation. | |
| Jul 1, 2015 at 17:11 | answer | added | Johannes Hahn | timeline score: 11 | |
| Jul 1, 2015 at 17:07 | comment | added | A Question Asker | Sorry, I meant a category that is a finite preorder (essentially 5 objects 1 through 5 which are a preorder). | |
| Jul 1, 2015 at 16:09 | comment | added | Todd Trimble | Well, the category of finite preorders is not a finite category, so I'm not sure what you're really after. The Monster group is an interesting finite category with one object and quite a few morphisms. The poset of truth values $\{0 \leq 1\}$ has a lot of nice properties (e.g., being cartesian closed) that are worth contemplating. Something that you might wish to contemplate is why the category of finite categories does not have coequalizers! | |
| Jul 1, 2015 at 15:57 | review | First posts | |||
| Jul 1, 2015 at 16:00 | |||||
| Jul 1, 2015 at 15:57 | history | asked | A Question Asker | CC BY-SA 3.0 |