Timeline for Are there any interesting classes of limits containing finite limits?
Current License: CC BY-SA 4.0
4 events
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| Mar 29 at 14:09 | comment | added | Denis T | @varkor I mean, the definition of L-finiteness, i. e. that terminal object in presheaves on C^op is compact (or, to explicate: representable functor which is represented by the terminal object in op-presheaves commutes with filtered colimits) does seem to produce saturated classes of diagrams if you replace "filtered" with other product-closed class of diagrams; but it doesn't seem true that if you begin with a class X, analogous "L-Xness" characterises the "limit centraliser". | |
| Mar 29 at 1:57 | comment | added | Tim Campion | I still don’t know what the spirit of the question is. It seems to me that pointing out that the class of finite categories is not already saturated is extremely relevant in the context of the question. | |
| Mar 27 at 10:04 | comment | added | varkor | While this is technically correct, I don't feel it is quite in the spirit of the question, since L-finite diagrams are the saturation of the finite diagrams, and so one doesn't obtain any new limits by considering them over the finite diagrams. | |
| Mar 26 at 18:02 | history | answered | Denis T | CC BY-SA 4.0 |