Talk:Thin category

A purist might insist that "posetal category" should not exist as a distinct term, since "preordered set" has exactly the same meaning (or "poset" assuming skeletality). However the term is in wide use, including in Wikipedia and hence allowing such uses to be a link. Moreover the information in this article would be out of place in preordered set as being too category-centric. --Vaughan Pratt (talk) 21:00, 31 March 2011 (UTC)

Alternatively one could simply replace the text of this article with a redirect to poset, but this might leave many readers in the dark. --Vaughan Pratt (talk) 21:26, 31 March 2011 (UTC)

I've never heard of "posetal category" used to mean "poset, regarded as a category". Also, it's quite different from a "thin category", which means "preordered set, regarded as a category". John Baez (talk) 18:39, 3 June 2019 (UTC)

As the above comment suggests, "posetal category" is uncommon and confusing since it indicates that the category is skeletal. Therefore I suggest moving the article to thin category. 慈居 (talk) 03:34, 8 May 2026 (UTC)

I support changing the article title and your improvements to the article. Thanks to your improvements to the article, the article is now ready to be moved.--SilverMatsu (talk) 05:35, 8 May 2026 (UTC)

When I searched on Google Scholar, the search results returned were: "Your search - "posetal category", "thin category" - did not match any articles published up to 2020." I support the name change, but it may not be necessary to redirect the posetal category to the thin category.--SilverMatsu (talk) 01:03, 10 May 2026 (UTC)

I personally prefer just to say "poset" (by taking and working on a universe) or "poset seen as category" when confusion may arise. For an article titled "thin category", perhaps "skeletal thin category" is fine enough. I am not familiar with the name "posetal category" and not sure what it means precisely, in particular whether it is assumed skeletal. Your serach result suggests that this is rarely used anyway. 慈居 (talk) 07:48, 10 May 2026 (UTC)

I'm also unsure whether "posetal category" means "thin category" or "poset seen as category," so I added the "citation needed" tag. If the term "posetal category" is removed from this article, we can move articles without leaving redirects by submitting a request at WP:RM/TR.--SilverMatsu (talk) 16:35, 11 May 2026 (UTC)

Support. The term "thin category" is probably more common (although it's the same thing as a preordered class). If I remember, Mac Lane calls this kind of category a "preorder" but that usage may not be standard. Taku (talk) 08:05, 10 May 2026 (UTC)

After checking the reference already present in this article, Roman (2017), it appears that "preordered category" and "thin category" are synonymous terms.--SilverMatsu (talk) 16:35, 11 May 2026 (UTC)