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I just added a link to Lurie's "What is...?" paper.
But note that that article is about $(\infty, 1)$-categories.
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.
Nice!
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.
Added the reference
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.
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.
moving all the old references on n-categories to n-category.
added pointer to:
added pointer to:
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