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May 10, 2011 at 13:14 comment added S. Carnahan This is not particularly important, but it might be good to change "begs the question" to "suggests the question", since the former is often used to mean something else.
May 9, 2011 at 13:40 vote accept David Carchedi
May 9, 2011 at 5:11 comment added David Roberts One thing you might consider (perhaps it is too strong) is using regular topological groupoids (as defined in Ehresmann's 1959 article on topological and smooth stacks. These have a nice structure theory analogous to Lie groupoids, but might be too restrictive for you purposes. As you might guess, these also use folations, in the sense that the fibres of the source and target maps give rise to folations of the arrow space. But check that article for precise definitions.
May 8, 2011 at 21:31 history edited David Carchedi CC BY-SA 3.0
added 8 characters in body
May 8, 2011 at 21:31 comment added David Carchedi @Chris: Yes, I meant to say representable epimorphism.
May 8, 2011 at 14:46 comment added Chris Schommer-Pries Surely you want the representable map $X \to \mathcal{X}$ to have some additional property like being surjective?
May 8, 2011 at 12:27 answer added André Henriques timeline score: 5
May 8, 2011 at 11:56 answer added Angelo timeline score: 8
May 8, 2011 at 10:47 history edited David Carchedi CC BY-SA 3.0
Added definition of topological stack
May 8, 2011 at 10:43 comment added David Carchedi Yes, depending on which article of his. I mean what he refers to as a "pretopological stack" in "Foundations of Topological Stacks I". I'll add this to the question.
May 8, 2011 at 4:21 comment added Angelo What do you mean by a topological stack? Is it in the sense of Noohi?
May 8, 2011 at 1:01 history asked David Carchedi CC BY-SA 3.0