Timeline for Do cocontinuous SET-valued functors separate points?
Current License: CC BY-SA 3.0
12 events
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| Jul 1, 2013 at 20:42 | comment | added | Theo Johnson-Freyd | Ah, great. I probably knew that at some point. | |
| Jul 1, 2013 at 18:40 | comment | added | Qiaochu Yuan | @Theo: a map is an epimorphism if and only if its cokernel pair (ncatlab.org/nlab/show/cokernel+pair) is trivial, which is a type of pushout. But yes, I also noticed later that you don't need that fact to show that $\mathbb{F}_p \to \emptyset$. | |
| Jul 1, 2013 at 17:59 | comment | added | Theo Johnson-Freyd | Then again, you only use "preserves epimorphisms" to show that $\mathbb F_p \mapsto \emptyset$, and this can be seen because the two inclusions $\mathbb F_p \to \mathbb F_p \otimes \mathbb F_p$ are isomorphisms. | |
| Jul 1, 2013 at 17:58 | comment | added | Theo Johnson-Freyd | I do like that your examples don't need* the cosheaf to be cocontinuous, but just to distribute over finite coproducts. (*Except for the question in my previous comment?) | |
| Jul 1, 2013 at 17:55 | comment | added | Theo Johnson-Freyd | Awesome. I should have thought of the $\mathrm{Vect}$ case. In Edit 2, maybe I'm being dumb, but why must a cosheaf preserve epimorphisms? Not every epimorphism is split, e.g. $\mathbb Z \to \mathbb Q$ is an epi in $\mathrm{CRing}$. | |
| Jul 1, 2013 at 15:56 | vote | accept | Theo Johnson-Freyd | ||
| Jul 1, 2013 at 8:22 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Jul 1, 2013 at 7:59 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Jul 1, 2013 at 7:49 | history | undeleted | Qiaochu Yuan | ||
| Jul 1, 2013 at 7:49 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Jul 1, 2013 at 7:31 | history | deleted | Qiaochu Yuan | ||
| Jul 1, 2013 at 7:28 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |