Timeline for Confusion in understanding the notion of $G$ Principal bundle where $G$ is a geometric group over a site
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| May 16, 2020 at 6:25 | comment | added | Adittya Chaudhuri | @MikeShulman Thank you Sir. I will definitely look at the portion of the paper you mentioned. I am apologising for writing clumsily in the comments . I will write my doubts clearly and post it as a separate question and will mention the link here. Thank you. | |
| May 15, 2020 at 23:38 | comment | added | Mike Shulman | I don't know what the point being made in of all your comments is; I was just saying that I think your original question is answered a few pages later in the paper. | |
| May 15, 2020 at 13:14 | comment | added | Adittya Chaudhuri | @MikeShulman In my 2nd comment there is a correction. The link I mentioned must be replaced by arxiv.org/abs/1207.0248 Thank you | |
| May 15, 2020 at 13:11 | comment | added | Adittya Chaudhuri | @MikeShulman Sir, should I ask these things separately in a new question? | |
| May 15, 2020 at 13:09 | comment | added | Adittya Chaudhuri | @MikeShulman I am also right now not that comfortable with the language of the paper arxiv.org/abs/0803.3692 due to use of infinity category. But I am very curious about connecting a link of how my understanding of Principal 2 bundles (in the sense of papers by Baez, schrieber, Wockel I mentioned above) with this paper on principal infinity bundles which treats the concept of principal 2 bundles as a particular case! | |
| May 15, 2020 at 13:04 | comment | added | Adittya Chaudhuri | @MikeShulman Now since I don't have have much background in infinity category I am not able to understand what geometric infinity group is!! I am also confused about the term geometric group . But it seems geometric 2 groups must be related to 2 groups (in the sense of arxiv.org/abs/math/0307200). Also since in the previous papers I mentioned about principal 2- bundles above they clear mentioned about their base (i.e some 2 space) but here I could not get what is the base of such Principal infinity bundles!! Is it some $(\infty,1)$ category? | |
| May 15, 2020 at 12:58 | comment | added | Adittya Chaudhuri | @MikeShulman Though Wockel mentioned about the general Principal 2 bundles but his treatment was mostly on what they called semi strict principal 2 bundle over a manifold(considered as a degenerate smooth 2 space). Though I don't have much background in infinity category but in the paper arxiv.org/abs/0803.3692 from the 4th paragraph in the 1st section it seems that Principal infinity bundles is a generalisation of Principal 2 bundles when the structure group is something like infinity space(which they called geometric infinity groups). | |
| May 15, 2020 at 12:52 | comment | added | Adittya Chaudhuri | @MikeShulman Sir, I came across the notion of Principal 2 bundles from Bartels 2 bundle's (arxiv.org/abs/math/0410328) where a principal 2 bundle is defined within a category internal to some generalised smooth space and the structure group is a coherent 2-group as introduced in arxiv.org/abs/math/0307200. Baez, Schrieber in arxiv.org/abs/hep-th/0412325 introduced a notion of connection in it but restricted the base to dengenerate smooth 2 space and Loop spaces. Wockel in arxiv.org/abs/0803.3692 also mentioned about Principal 2 bundles. | |
| May 15, 2020 at 1:10 | comment | added | Mike Shulman | Did you try reading beyond the first paragraph of the first section? | |
| May 1, 2020 at 9:13 | history | edited | Adittya Chaudhuri | CC BY-SA 4.0 |
added 280 characters in body
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| May 1, 2020 at 9:03 | history | asked | Adittya Chaudhuri | CC BY-SA 4.0 |