Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 9th 2013
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 9th 2013

    I have changed

    A continuous category is a categorification of the notion of continuous poset.


    The notion of continuous category is a categorification of the notion of continuous poset.

    • CommentRowNumber3.
    • CommentAuthorRodMcGuire
    • CommentTimeJul 9th 2013

    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. ]

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJul 10th 2013

    I think the usual encoding of parentheses is %28 and %29.

    • CommentRowNumber5.
    • CommentAuthorRodMcGuire
    • CommentTimeJul 11th 2013

    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).

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2013

    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?

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeJul 12th 2013

    Humans try to read URLs?

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2013
    • (edited Jul 12th 2013)

    By necessity so for instance in non-html emails, on G+, etc. yes.

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeJul 12th 2013

    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.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2013

    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.

    • CommentRowNumber11.
    • CommentAuthorTobyBartels
    • CommentTimeJul 21st 2013
    • CommentRowNumber12.
    • CommentAuthormaxsnew
    • CommentTimeJun 14th 2018

    Include a useful characterization of continuous categories from Johnstone-Joyal

    diff, v12, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2018
    • (edited Jun 14th 2018)

    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 CC is continuous if and only if it is a retract of a category Ind(D)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…)

    • CommentRowNumber14.
    • CommentAuthormaxsnew
    • CommentTimeJun 14th 2018

    Cite Johnstone-Joyal

    diff, v14, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2018


    I have added reference-anchor and hyperlink:

      ([Johnstone-Joyal 82, Theorem 2.8](#JohnstoneJoyal82))

    such that it now comes out as

    (Johnstone-Joyal 82, Theorem 2.8)

    • CommentRowNumber16.
    • CommentAuthormaxsnew
    • CommentTimeJun 14th 2018

    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?

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2018

    Good point. It seems this was missing. I have now added something to the HowTo-page:

    How to cite and record references

    • CommentRowNumber18.
    • CommentAuthormaxsnew
    • CommentTimeJun 14th 2018

    Thanks, very helpful!

    • CommentRowNumber19.
    • CommentAuthorDmitri Pavlov
    • CommentTimeOct 14th 2022


    The setting of (∞,1)-categories

    Continuous (∞,1)-categories are introduced under the name of compactly assembled ∞-categories in Lurie [{#SAG}, §21.1.2].

    diff, v17, current

    • CommentRowNumber20.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 17th 2022

    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.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)