Talk:Weak n-category

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No! Merging into quasi-category is not appropriate! A quasi-category is a

special $\infinity$-category where all $k$-morphism for $k>1$ are equivalences.

That need not to be the case with weak $n$-categories. So it is a very different story.

Requested move 1 May 2025

:Weak n-category → {{no redirect|n-category}} – This is a proposal to rename the article to "n-cateogry" as well as to move the materials on a strict n-category from higher category theory to here. The reason: while there is a genuine difference, a strict n-cateogry and a strict n-weak category are both an attempt to articulate the concept of an n-cateogry. And, in general, the conceptual side should triumph against the strict mathematical definition side. That attitude is actually common in Wikipeida; when there are some variants in definitions, we don't create separate articles depending on variations. Also, discussing strict and weak versions at the same place should make it easier to discuss stuff like coherent theorems. Taku (talk) 06:38, 1 May 2025 (UTC)

:I think weak and strict n-categories deserve separate articles. To quote [https://mathoverflow.net/questions/233627/how-to-stop-worrying-about-enriched-categories#comment578175_233640 Todd Trimble], even for $n=2$ , although every bicategory is biequivalent to a strict 2-category, that doesn't mean the tricategory of bicategories is triequivalent to the strict 3-category of strict 2-categories. I'm also worried that it would take up too much space to cover both of them. The theory of strict n-categories is much simpler, but one may not be satisfied with brief notes on the difference of weak and strict cases.

:I do think n-category can serve as a gentle conceptual introduction to higher categories and I'm fine with moving materials from other articles to there for now if you want to proceed with it. But I suggest leaving there the possibility of separate articles for weak and strict n-categories. 慈居 (talk) 01:23, 7 May 2025 (UTC)

::I do agree that there are various technical matters that are best left to separate specialized articles. On the other hand, concepts like weak n-category only make sense to those who have an idea of an n-category and currently we don't have an article on it. It's usually better to have an article covering a broad idea first and then, when necessary, leave detailed technical aspects to specialized articles. After all, strict, weak, semi-strict etc n-categories are all various ways to articulate a concept of an n-category in some ways. -- Taku (talk) 06:31, 7 May 2025 (UTC)