Timeline for 2-colimits in the category of cocomplete categories
Current License: CC BY-SA 3.0
11 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| May 29, 2011 at 10:32 | vote | accept | Martin Brandenburg | ||
| May 25, 2011 at 21:35 | answer | added | Mike Shulman | timeline score: 12 | |
| May 16, 2011 at 20:55 | comment | added | Zoran Skoda | Write an email to Steve Lack, he is likely to know if it is known. | |
| May 16, 2011 at 11:20 | comment | added | Martin Brandenburg | I think I can construct $2$-coproducts in $\text{Cat}_c$, but I don't know how to deal with coequalizers. Also, everything becomes more mysterious in the enriched setting, say with $R$-linear categories. In the details, the whole thing becomes even more fiddly. Is the answer to my question unknown, or is it just a "common fact"? | |
| May 15, 2011 at 21:18 | comment | added | Zoran Skoda | Here is an idea. The forgetful functor is not only having a left adjoint but is in fact 2-monadic (see Kelly and Lack emis.dsd.sztaki.hu/journals/TAC/volumes/7/n7 and references therin). Now monadic functors create and preserve limits but not colimits. However, if you have coequalizers (not preserved!) then in 1-categorical situation you can construct colimits on the Eilenberg-Moore category, cf. Borceux, Handbook vol. 2, Prop. 4.3.4. So if you can make coequalizers and the Prop. extends to 2-dim situation you are in business. | |
| May 14, 2011 at 21:45 | history | edited | Martin Brandenburg | CC BY-SA 3.0 |
added 99 characters in body
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| May 14, 2011 at 17:20 | comment | added | Martin Brandenburg | Thank you. The work is interesting, but it is not useful in this situation. | |
| May 14, 2011 at 13:36 | comment | added | Zoran Skoda | Martin, for your purposes which I am guessing, maybe the work of Durov on vectoids could be also useful. I have sent you some data via personal email. | |
| May 14, 2011 at 13:28 | comment | added | Zoran Skoda | Similar issues are discussed in the papers relating to "totality" in category theory (look e.g. for Max Kelly's articles). Off hand, I do not know the precise answer. | |
| May 14, 2011 at 11:59 | history | asked | Martin Brandenburg | CC BY-SA 3.0 |