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    • CommentRowNumber1.
    • CommentAuthoradeelkh
    • CommentTimeDec 20th 2012


    I just added a link to Lurie's "What is...?" paper.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 20th 2012

    But note that that article is about (,1)(\infty, 1)-categories.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 20th 2012
    • (edited Dec 20th 2012)

    Thanks Adeel! We were indeed lacking that reference.

    While David is of course right about what he says above, on the other hand our old and woefully neglected entry ∞-category didn’t really make that clear at all, nor did it really point to (∞,1)-category.

    I have now added a few paragraphs to the Idea-section at ∞-category that try to amplify that the term “\infty-category” is used to mean two rather different things, and that one of these meaning is discussed not in this entry, but in (∞,1)-category.

    I also moved the What is…-reference to (∞,1)-category.

    • CommentRowNumber4.
    • CommentAuthoradeelkh
    • CommentTimeDec 21st 2012


  1. Fixed the link to “Higher-Dimensional Categories: An Illustrated Guidebook” (now at Eugenia Cheng’s personal website, no longer at Sheffield).

    Arne Hofmann

    diff, v32, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 3rd 2021

    To avoid this “link rot” of references I have adopted the habit of uploading to the nLab server non-stably hosted author pdf-s that I care about.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 31st 2024

    Added the reference

    • Zach Goldthorpe, Homotopy theories of (,)(\infty,\infty)-categories as universal fixed points with respect to enrichment [arXiv:2307.00442]

    Do we still want to say the following?:

    While there are several existing proposed definitions for what a single ∞-category is, in the most general sense, there is no real understanding of the correct morphisms between them, hence of the correct (∞,1)-category of ∞-categories. But this may of course change with time.

    diff, v34, current

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJan 31st 2024
    • (edited Jan 31st 2024)

    This article is strange. I propose to make it a disambiguation page for (∞,1)-category and (∞,∞)-category, and most of the material can be moved to (∞,∞)-category.

    In fact, we do not have a separate article for (∞,∞)-categories, and the term redirects to this page. So perhaps this article could be renamed to (∞,∞)-category, and a new disambiguation page ∞-category could be created then.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2024

    I have cleared this old entry and added a few new paragraphs from scratch. This leaves much room for further expansion.

    diff, v35, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2024

    moving all the old references on n-categories to n-category.

    diff, v35, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeFeb 16th 2024
    • (edited Feb 16th 2024)

    added pointer to:

    • Félix Loubaton, Theory and models of (,ω)(\infty,\omega)-categories [arXiv:2307.11931]

    diff, v36, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeMar 12th 2024

    added pointer to:

    diff, v37, current