Timeline for Compare three 2-categories of (Lie) groupoids
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 28, 2023 at 6:30 | comment | added | David Roberts♦ | @TheAmplitwist I believe the paper is: Colman, H. On the 1-Homotopy Type of Lie Groupoids, Appl. Categor. Struct, 19 (2011) pp 393–423, doi.org/10.1007/s10485-010-9227-y (I don't see another paper by Colman in a Springer journal published before 2011) | |
| Feb 14, 2023 at 8:57 | comment | added | The Amplitwist |
The link to springerlink.com is broken. I'm also unable to find any snapshot saved on the Wayback Machine.
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| Dec 5, 2011 at 0:44 | comment | added | David Roberts♦ | Sorry for not replying earlier! In regards to your 22Nov question, you really don't want to use 'weak pullbacks' (really they are isocomma objects), that is the approach used in Pronk's paper, and one reason why the 2-cells are so complicated. The advantage of anafunctors is that using the strict pullback (using the pretopology that one has) means you get representatives of 2-cells instead of using equivalence classes. | |
| Dec 4, 2011 at 14:18 | comment | added | Ma Ming | @David Roberts I am wondering what is the horizontal composition of (internal) anafunctors. It seems not given in the your article or Toby Bartels' thesis that you refereed to. | |
| Nov 22, 2011 at 16:28 | comment | added | Ma Ming | @David Roberts May I ask a question, What is the result if one use weak pullbacks to define 2-morphisms of anafunctors? | |
| Nov 22, 2011 at 8:58 | comment | added | Ma Ming | I read this paper several days ago, nice 2 c u! | |
| Nov 22, 2011 at 1:23 | comment | added | David Roberts♦ | I should say that all of these are all models for 'the' bicategorical localisation of LieGpd at the weak equivalences. Concerning the equivalence between the different sort of 2-morphisms, Makkai in his paper on anafunctors essentially proves that the more general 2-arrows in (1'), when restricted to between the 1-arrows of (2) (which are secretly a special case of (1')), are in bijective correspondence with the 2-arrows of (2). | |
| Nov 22, 2011 at 1:20 | comment | added | David Roberts♦ | May I advertise my article ncatlab.org/davidroberts/files/DRoberts_anafunctors.pdf (an update of arxiv.org/abs/1101.2363, although it is still more improved in the latest version, not yet public) which provides another model (actually a family of such), equivalent to the above? Proposition 6.5 in my paper (proved by Pronk) is what you can use to see that all these are equivalent. (Edit 2023 - the paper was published in 2012 as tac.mta.ca/tac/volumes/26/29/26-29abs.html) | |
| Nov 21, 2011 at 17:11 | history | edited | Ma Ming | CC BY-SA 3.0 |
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| Nov 21, 2011 at 16:41 | answer | added | David Carchedi | timeline score: 8 | |
| Nov 21, 2011 at 15:10 | history | edited | Ma Ming | CC BY-SA 3.0 |
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| Nov 21, 2011 at 15:02 | history | asked | Ma Ming | CC BY-SA 3.0 |