Timeline for On limits and Colimits
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 24, 2015 at 22:07 | comment | added | Todd Trimble | This question would probably be closed quickly if it were asked today, but it's strange no one gave a complete answer to the general non-existence for the first case. Consider the ordered set $[0, 1]$ as a category in the usual way posets are considered categories, and let $A = 1$ and take $B_i = 1 - 1/i$ with index $i = 1, 2, 3, \ldots$. Then $\text{Hom}(A, \text{colim} B_i)$ is a singleton, whereas $\text{lim}\; \text{Hom}(A, B_i)$ is empty, so there is no such map. In the case for abelian groups, of course such a morphism exists since we have zero morphisms! | |
| Dec 24, 2015 at 19:09 | history | edited | David White | CC BY-SA 3.0 |
Fixed typos and texified, since it was on the front page anyway
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| Dec 24, 2015 at 18:10 | history | edited | user9072 |
edited tags
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| Dec 13, 2009 at 2:08 | vote | accept | Shizhuo Zhang | ||
| Dec 12, 2009 at 16:40 | comment | added | Kim Morrison | @Shizhou, if you intend these objecs to be abelian groups, you should say so in the question. (cf your comment below.) | |
| Dec 12, 2009 at 13:09 | answer | added | Leonid Positselski | timeline score: 22 | |
| Dec 12, 2009 at 12:59 | comment | added | Harry Gindi | The existence of that morphism is trivial and I'm pretty sure that's not what he's looking for. | |
| Dec 12, 2009 at 12:55 | comment | added | Leonid Positselski | No, he is asking about morphisms, not isomorphisms. So the first formula is indeed wrong, but the morphism in the second formula does actually exist. Neither it matters whether the colimit in the second formula is finite or infinite. The morphism exists in both cases, and it is not an isomorphism, in general, in both cases. | |
| Dec 12, 2009 at 12:48 | comment | added | Shizhuo Zhang | I am sorry for the misprints,I have corrected | |
| Dec 12, 2009 at 12:45 | answer | added | Harry Gindi | timeline score: 4 | |
| Dec 12, 2009 at 12:44 | history | edited | Shizhuo Zhang | CC BY-SA 2.5 |
edited body; added 3 characters in body
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| Dec 12, 2009 at 12:44 | comment | added | Leonid Positselski | I would suggest that you reread what you have written and correct the misprints, for starters. The first would-be morphism does not make much sense due to some mixup between lim and colim, apparently. In the second one, one "Hom" is missing and there is a misprint "B1". | |
| Dec 12, 2009 at 12:14 | history | asked | Shizhuo Zhang | CC BY-SA 2.5 |