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nLab > Latest Changes: quotient stack

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 10th 2013

    I noticed that there was no entry quotient stack, so I quickly started one, just to be able to point to it from elswhere.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeFeb 26th 2018

    The idea of quotient stack extended in a standard way using general internal groupoids in a site or topos.

  3. I have added motivation for definition of quotient stack

    diff, v10, current

    • CommentRowNumber4.
    • CommentAuthorAli Caglayan
    • CommentTimeDec 19th 2018

    changed // to \sslash

    diff, v12, current

    • CommentRowNumber5.
    • CommentAuthorAli Caglayan
    • CommentTimeDec 19th 2018
    • (edited Dec 19th 2018)

    changed // to \sslash

    diff, v12, current

    nevermind \sslash doesn’t work on nlab for some reason. Changed them back

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 20th 2018

    In principle it works and is being used. But there may be a font issue. For me it works on Firefox on Windows.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 20th 2018

    It’s a problem with Chrome again.

  8. Universal property (??) for Quotient stack. Comments are welcome.

    diff, v13, current

  9. Tried to clean up the wording, make a few things slightly more precise, and separate the two different notions of “principal G-bundle” appearing.

    D. Zack Garza

    diff, v16, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeApr 15th 2023

    added references for the common construction of quotient stacks X⫽GX\sslash G via prestacks of GG-principal bundles equipped with GG-equivariant maps to XX:

    (there must be more canonical references for this construction – if anyone has a good reference at hand, let’s add it!)

    and pointer to this recent discussion of sufficient conditions for this construction to really yield a stack (instead of just a prestack):

    diff, v17, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023

    added pointer to:

    diff, v18, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023

    added pointer to:

    diff, v18, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023

    added pointer to

    for the definition of quotient stacks as stackifications of ((2,1)-presheaves of) action groupoids

    diff, v19, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023

    also pointer to:

    diff, v20, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023
    • (edited Apr 16th 2023)

    I have finally looked at the section here which Praphulla Koushik had announced in message #8 above (Dec. 2018), asking for comments.

    Now I see that this section is trying to get at the characterization of GG-quotient stacks as fibrations over BG\mathbf{B}G. So I have added references which discuss this perspective (now here – these are the pertinent references that I am aware of; if there are others let’s add them in, too).

    I haven’t yet touched Praphulla’s section itself (there is room to bring it into a state which would allow removing the question marks) except for prefixing it by a pointer to these references.

    diff, v20, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeJun 1st 2023

    added publication data for this item:

    diff, v21, current

    • CommentRowNumber17.
    • CommentAuthorzskoda
    • CommentTimeJun 1st 2023

    15: the section looks correct to my reading and present knowledge.

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