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I have changed
A continuous category is a categorification of the notion of continuous poset.
to
The notion of continuous category is a categorification of the notion of continuous poset.
Enhanced the reference to:
Peter Johnstone and Andre Joyal, Continuous categories and exponentiable toposes, JPAA 25 (1982), doi (free PDF)
I checked the PDF link there and it is not stable so it can’t be directly linked. Is this a good convention to indicate that the PDF is freely available on the page the DOI takes you to?
[ AARGH: In the nLab I was unable to figure out how to escape the parens in the DOI URL so I had to revert to “a href=” syntax. Strangely in the nForum those parens cause no problem. ]
I think the usual encoding of parentheses is %28 and %29.
Ok, URL percent encoding seems to work both in the fixed nLab entry and the nForum
Peter Johnstone and Andre Joyal, Continuous categories and exponentiable toposes, JPAA 25 (1982), doi (free PDF)
though I don’t understand why it isn’t required in the nForum but is in the nLab (or where this might be documented).
By the way, on something mildly related: on my end this encoding has the annoying consequence that it messes up all url-s that I copy and paste for peaople to read. Often I copy-and-paste nLab entry URLs into emails or into other online forums in plain text, and then all those percent signs make them unreadable for humans.
Is there a quick way to deal with this? How do you all do this?
Humans try to read URLs?
By necessity so for instance in non-html emails, on G+, etc. yes.
Even if you get a URL in a plain text email and your email reader doesn’t automatically make it a link (which many will), you can copy and paste it into a browser without having to “read” it.
The thing is I write to people “see here: …” and then follows unreadable code they don’t know where I am pointing them to. If I write “see here: …” and there is a readable url, then they know what I am doing to them, and can remember it.
This happens to me all the time. I spend lots of time undoing percent-encoding for such messages,
But if you don’t need this, that’s fine with me. My question is purely technical: if anyone konws how to copy-and-paste URLs while avoiding the automatic percent-encoding.
Maybe this helps: http://www.url-encode-decode.com/?
I have added hyperlinks to the keywords, so that readers who don’t already know this stuff can still benefit:
In general, a locally small category $C$ is continuous if and only if it is a retract of a category $Ind(D)$ of ind-objects, where the functors exhibiting the retract preserve filtered colimits.
Please also add the pointer to Johnstone-Joyal! (unless you are going to write out the proof here…)
Thanks!!
I have added reference-anchor and hyperlink:
([Johnstone-Joyal 82, Theorem 2.8](#JohnstoneJoyal82))
such that it now comes out as
Thanks Urs, I didn’t know the “correct” formatting for citations on the nlab, or else I would have done it in my first edit. Is there a page that describes this sort of thing?
Good point. It seems this was missing. I have now added something to the HowTo-page:
Thanks, very helpful!
Added:
Continuous (∞,1)-categories are introduced under the name of compactly assembled ∞-categories in Lurie [{#SAG}, §21.1.2].
Can someone add something on why one might be interested in continuous categories? The Idea section merely refers to categorification of continuous poset, which just goes straight into a definition.
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