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I noticed that there was no entry quotient stack, so I quickly started one, just to be able to point to it from elswhere.
The idea of quotient stack extended in a standard way using general internal groupoids in a site or topos.
In principle it works and is being used. But there may be a font issue. For me it works on Firefox on Windows.
It’s a problem with Chrome again.
added references for the common construction of quotient stacks $X\sslash G$ via prestacks of $G$-principal bundles equipped with $G$-equivariant maps to $X$:
Jochen Heinloth, Exp. 1.5 in: Notes on differentiable stacks (2004) [pdf]
Frank Neumann, p. 28 in: Algebraic Stacks and Moduli of Vector Bundles, impa (2011) [pdf, pdf]
(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):
added pointer to:
added pointer to:
added pointer to
for the definition of quotient stacks as stackifications of ((2,1)-presheaves of) action groupoids
also pointer to:
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 $G$-quotient stacks as fibrations over $\mathbf{B}G$. 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.
added publication data for this item:
15: the section looks correct to my reading and present knowledge.
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