Timeline for Comparing discrete fibrations and their duals
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 13, 2011 at 23:42 | comment | added | Steve Lack | Yes, Mike, quite right - the equivalence of discrete fibrations and codiscrete cofibrations is an exactness condition which will carry over to Cat-valued presheaves. And I'd guess Grothendieck 2-toposes should work as well, although I haven't checked the details. | |
| May 13, 2011 at 13:20 | comment | added | Mike Shulman | What about 2-categories of Cat-valued (2-)presheaves? Since all these notions can be defined in terms of limits and colimits, I would expect them to carry over pointwise. And if that works, then what about Grothendieck 2-topoi (left exact reflective sub-2/bi-categories of Cat-valued presheaf categories)? | |
| May 12, 2011 at 1:50 | vote | accept | Finn Lawler | ||
| May 11, 2011 at 23:35 | comment | added | Steve Lack | First question: yes (sorry, that was unclear). Second question: no (but if I think of one I'll let you know). | |
| May 11, 2011 at 17:51 | comment | added | Finn Lawler | OK, thanks. So the correspondence in the case of Cat really is a red herring. When you say 'the 2-category A has an underlying ordinary category which is discrete', do you mean by A the total 2-category of a fibration from 1 to 1? Also, (I know it's unlikely but) are there, to your knowledge, any references that compare the two notions in detail? | |
| May 11, 2011 at 12:12 | history | answered | Steve Lack | CC BY-SA 3.0 |