Timeline for Applications of lax 2-limits which are not pseudo 2-limits
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Jan 6, 2011 at 2:47 | comment | added | Nic Palmero | Of course every pseudo functor is a lax 2-functor, so your claiming that it cannot be a lax 2-limit (without changing its weighting)? | |
| Jan 5, 2011 at 20:45 | answer | added | Mike Shulman | timeline score: 8 | |
| Jan 5, 2011 at 20:36 | comment | added | Mike Shulman | No, a comma category is not a lax 2-limit. It is a weighted (pseudo) 2-limit. See nlab.mathforge.org/nlab/show/2-limit#lax. | |
| Jan 5, 2011 at 16:40 | comment | added | Nic Palmero | After your remark about the comma category (which contains the notion of slice category), it occurred to me that there is a natural application of lax 2-colimits in the bicategory of topoi, viz., the famous "Medaille en Or" exercise from SGA4.1, Exp. IV, exercice I.4.10, one major application of which is to relate the sheaves on the crystalline site to the Zariski localisations of suitable thickenings (cf. Berthelot's thesis, chp. III). Cisinski and Baez also discussed the relation of the petit/gros topos in 2009 on the n-category cafe also. | |
| Jan 5, 2011 at 14:59 | comment | added | Nic Palmero | Yes it is; it's a weighted lax 2-limit. | |
| Jan 5, 2011 at 13:31 | comment | added | Harry Gindi | Isn't the comma category some kind of lax 2-limit? | |
| Jan 5, 2011 at 13:28 | history | edited | Nic Palmero | CC BY-SA 2.5 |
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| Jan 5, 2011 at 7:40 | history | edited | Nic Palmero | CC BY-SA 2.5 |
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| Jan 5, 2011 at 5:52 | history | asked | Nic Palmero | CC BY-SA 2.5 |