Timeline for Subcategories of abelian categories generated by finitely many objects
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2012 at 16:35 | history | edited | Jeff Strom | CC BY-SA 3.0 |
"to many" changed to "too many"
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| Mar 14, 2012 at 3:03 | comment | added | Theo Johnson-Freyd | If you have a fixed ambient category, there is no reason to worry about objects only being defined up to isomorphism. It is very reasonable to consider only those subcategories that are "closed under isomorphism": if $X$ is in your subcategory and $X \overset\sim\to Y$ in your ambient category, then demand that $Y$ is in your subcategory. You should also of course demand that the subcategory be full. | |
| Mar 13, 2012 at 19:26 | answer | added | Eric Wofsey | timeline score: 8 | |
| Mar 13, 2012 at 17:45 | comment | added | Tom Leinster | There was a similar terminological discussion here: mathoverflow.net/questions/86090 | |
| Mar 13, 2012 at 16:46 | answer | added | Martin Brandenburg | timeline score: 2 | |
| Mar 13, 2012 at 15:57 | comment | added | JvW | Oh yeah, sorry I didn't mention that the subcategory should be abelian. I see the problem with the distinction between sub-abelian categories and abelian subcategories. Haven't thought about it before. I guess I would prefer the subcategories to abelian subcategories, but I guess an answer to either would help me to understand the task better. | |
| Mar 13, 2012 at 15:52 | history | edited | JvW | CC BY-SA 3.0 |
added 12 characters in body
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| Mar 13, 2012 at 15:44 | comment | added | Qiaochu Yuan | I'm not sure I understand exactly what you want to do. You want the smallest subcategory containing one object $X$ and all endomorphisms of $X$. Okay, so just take the category consisting of $X$ and all of its endomorphisms. If you mean something else by subcategory, then what? If I'm not horribly mistaken, you need to distinguish between "abelian subcategory" and "sub-abelian category" because in the former the kernels, cokernels, etc. don't need to agree with those in the ambient category (or something like that). | |
| Mar 13, 2012 at 14:57 | history | asked | JvW | CC BY-SA 3.0 |