Timeline for Is $\text{Ind-}\bf C$ the category of models for a sketch?
Current License: CC BY-SA 3.0
9 events
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| Oct 27, 2013 at 13:32 | comment | added | Todd Trimble | @tetrapharmakon I already did that. Her viva (thesis examination) should be coming up within the next few months, and she said that after submitting any corrections after the examination and gaining final acceptance, she'd be happy to make the thesis available to interested people. | |
| Oct 27, 2013 at 13:02 | comment | added | fosco | In this case I will be glad to accept Karol's answer if he decides to rewrite his comment. :) I was strongly encouraged by O. Caramello to contact Marie via email to ask for a copy of its thesis. Can't wait for the answer! | |
| Oct 26, 2013 at 21:58 | comment | added | Todd Trimble | @tetrapharmakon I disagree it should be closed as a duplicate! The context is a little different, so we should let this stand. I for one learned of a paper I was unaware of before, even though the paper was mentioned in the other thread, and I think the other question has not been addressed yet to 100% satisfaction -- still waiting to hear back from Marie Bjerrum!!. | |
| Oct 26, 2013 at 21:50 | comment | added | fosco | @Karol and Todd: thank you for your answer. The spirit of my question was exactly that of this other topic mathoverflow.net/questions/93262/… so I think this question can be closed as a duplicate. | |
| Oct 26, 2013 at 18:25 | comment | added | Todd Trimble | @KarolSzumiło Thank you; I wasn't quite sure what the question was when I first answered. If you post your comment as an answer, I'd gladly upvote it. Here is a link: sciencedirect.com/science/journal/00224049/175/1 | |
| Oct 26, 2013 at 18:02 | comment | added | Karol Szumiło | The paper Adámek, Borceux, Lack, Rosický, A classification of accessible categories addresses exactly these types of questions. In particular, Section 3 is about the Ind construction and Section 4 is about sketches. Everything is relative to some nice class of small categories $\mathbb{D}$ and these colimits that commute with $\mathbb{D}$-limits. | |
| Oct 26, 2013 at 15:58 | comment | added | fosco | Consider for example, aside to Ind_k(C), the case where A=sifted categories. Then B is the class of all discrete categories, and the completion of C with respect to sifted colimits is the category of models for the sketch having discrete cats as set of colimits (hope I didn't dualize too much times!) | |
| Oct 26, 2013 at 15:55 | comment | added | fosco | It seems possible to generalize this result: let A, B collections of small categories. Then Ind_A(C) (the completion of C with respect to A-shaped diagrams) is the category of models for the sketch having B as class of colimits iff any A-colimit commutes with any B-limit (I hope notations are clear with a little effort: comments force to a really dry exposition!) Are you aware of something at this level of generality? | |
| Oct 26, 2013 at 15:22 | history | answered | Todd Trimble | CC BY-SA 3.0 |