Timeline for Is the bounded derived category of coherent sheaves of a variety a small category?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 14, 2012 at 19:02 | comment | added | David Steinberg | The short answer is that epimorphisms of my abelian category are more easily understood if I can think of them as epimorphisms of modules. | |
| Feb 14, 2012 at 18:45 | vote | accept | David Steinberg | ||
| Feb 14, 2012 at 11:59 | comment | added | Yosemite Sam | out of curiosity: how does the Freyd-Mitchell embedding make life much easier? | |
| Feb 14, 2012 at 3:53 | comment | added | B. Bischof | Another term for essential small is "svelte": ncatlab.org/nlab/show/svelte+category | |
| Feb 14, 2012 at 3:20 | comment | added | David Steinberg | @Qiaochu: yes, thank you: the term I want is essentially small. | |
| Feb 14, 2012 at 2:52 | comment | added | Qiaochu Yuan | The term you actually want is "essentially small" (equivalent to a small category). | |
| Feb 14, 2012 at 2:09 | answer | added | S. Carnahan♦ | timeline score: 5 | |
| Feb 14, 2012 at 0:03 | comment | added | Donu Arapura | Presumably small should be understood up to equivalence. I agree with Fernando, although writing down the details would entail some work: Choose a finite affine cover $\{Spec A_i\}$. Then a bounded complex of coherent sheaves is given by a collection of finitely presented $A_i$ modules $M_i^\bullet$ plus patching data. A morphism is ... | |
| Feb 13, 2012 at 20:33 | comment | added | algori | Fernando -- there may be an issue there, similar to the fact that the category of finite-dimensional vector spaces over a field $k$ is not itself small but is equivalent to the small category with $k^n$'s as objects. | |
| Feb 13, 2012 at 20:18 | comment | added | Fernando Muro | Of course it is, you can easily find a (transfinite) upper bound for the 'number' of objects | |
| Feb 13, 2012 at 20:13 | history | asked | David Steinberg | CC BY-SA 3.0 |