Timeline for Van Kampen colimits
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 25, 2015 at 10:01 | vote | accept | Michal R. Przybylek | ||
| Jun 25, 2015 at 0:44 | answer | added | Marc Hoyois | timeline score: 5 | |
| Jun 24, 2015 at 18:18 | comment | added | Joonas Ilmavirta | If the question is based on a confusion, telling exactly what the confusion was is a good answer. A question can be nonsensical in a strict sense (due to a confusion or a soft formulation) but still useful. I think such questions can (and should, provided they are otherwise good) be answered, although answering doesn't mean the same thing as for some other questions. There seems to be a confusion worth clarifying here, and an answer would probably convey that best to a future reader. | |
| Jun 24, 2015 at 17:48 | comment | added | Michal R. Przybylek | @JoonasIlmavirta, I am afraid some people are overenthusiastic about the moderation toolbox. Yes, I wanted to remove the question from both "unanswered" and "open" question lists. In fact, I would have deleted the question itself, if it were not for Marc Hoyois, who offered me his time. I think it is fair to keep the track of the conversation. On the other hand, it is clear that my question based on some terminological confusion and therefore, strictly speaking, it cannot be answered --- because there can be no answer to a no-question. | |
| Jun 24, 2015 at 16:16 | comment | added | Joonas Ilmavirta | If you want to remove your question from the unanswered list by providing a CW answer yourself (which is a good idea if it was answered in the comments), I suggest summarizing what the answer to the question is. Your current answer does answer the question and may be deleted because of that. If some comments answer your question, you can copy the comments to your answer (with suitable attribution and reformatting). | |
| Jun 23, 2015 at 15:46 | comment | added | Michal R. Przybylek | If you post your observations as an answer than I will be happy to accept it. | |
| Jun 23, 2015 at 15:41 | comment | added | Michal R. Przybylek | @ZhenLin, MarcHoyois --- that's right. Somehow I thought that if you strictify a pseudofunctor, then the concept of limits strictifies automatically. But it seems that it strictifies only in one direction. Hm... I just have unlearned something... | |
| Jun 23, 2015 at 14:55 | comment | added | Zhen Lin | @MarcHoyois It appears to me that Michal R. Przybylek is talking about 2-(co)limits in the classical sense of ($\mathbf{Cat}$-)enriched category theory, whereas you are talking about bi(co)limits. | |
| Jun 22, 2015 at 23:30 | comment | added | Marc Hoyois | Maybe your notion of 2-limit is different. According to the nLab definition ncatlab.org/nlab/show/2-limit, the inclusion Set → Cat does not preserve 2-colimits: the 2-colimit of $*\rightrightarrows *$ in Cat is the groupoid $B\mathbb{Z}$. Hence, the 2-limit of $Set\rightrightarrows Set$, where both arrows are the identity, is the category of $\mathbb{Z}$-sets. | |
| Jun 22, 2015 at 22:06 | history | rollback | Michal R. Przybylek |
Rollback to Revision 1
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| Jun 22, 2015 at 22:04 | comment | added | Michal R. Przybylek | @MarcHoyois, no, wait, I'm having hard moments today --- we are talking about discrete colimits, which are the same as in Cat (since the inclusion Set ---> Cat is left adjoint). So, what is your counterexample? BTW, we do not have to talk about 2-limits in Cat, because every limit in Cat is automatically a 2-limit. | |
| Jun 22, 2015 at 21:57 | history | undeleted | Michal R. Przybylek | ||
| Jun 22, 2015 at 21:20 | history | deleted | Michal R. Przybylek | via Vote | |
| Jun 22, 2015 at 21:19 | history | edited | Michal R. Przybylek | CC BY-SA 3.0 |
Error spotted by Marc Hoyois in the question
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| Jun 22, 2015 at 21:13 | comment | added | Michal R. Przybylek | @MarcHoyois, right --- because colimits in Set are not the same as colimits in Cat. Silly me :-) | |
| Jun 22, 2015 at 21:11 | comment | added | Marc Hoyois | In fact, the only locally presentable category in which all colimits are van Kampen is the terminal category, since such a category must be an $\infty$-topos. | |
| Jun 22, 2015 at 21:06 | comment | added | Marc Hoyois | The exponential functor $\mathbf{Set}^{(-)}$ does not send colimits of sets to 2-limits of categories. For example, consider the coequalizer of the diagram $*\rightrightarrows *$. | |
| Jun 22, 2015 at 19:37 | comment | added | Finn Lawler | arxiv.org/abs/1101.4594 ? | |
| Jun 22, 2015 at 18:44 | history | asked | Michal R. Przybylek | CC BY-SA 3.0 |