User talk:TakuyaMurata

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Coherence theorem for bicategory and 2-Yoneda lemma

I added the Coherence theorem to the 2-category, but perhaps it would be better to move it to the application section of the 2-Yoneda lemma? Also, does 2-Yoneda lemma refer to the Yoneda lemma for bicategory or the Yoneda lemma for strict 2-category? SilverMatsu (talk) 03:24, 27 April 2025 (UTC)[reply]

First, I think the coherence theorem makes much more sense in the 2-category article since it's about comparing weak and strict versions. Second, if I am not mistaken, I think the 2-Yoneda should work both for strict and weak 2-categories but the article should probably clarify that (this is why the proof is sketch.) -- Taku (talk) 07:22, 27 April 2025 (UTC)[reply]

I see. Thank you for explaining it to me.--SilverMatsu (talk) 09:16, 27 April 2025 (UTC)[reply]

Just let you know, wikipedia has Tricategory and 3-category is a redirect to Strict higher categories. In other words, weak 3-category and strict 3-categories seem to be separate articles.SilverMatsu (talk) 10:19, 27 April 2025 (UTC)[reply]

Maybe we don’t need separate articles 3-categories (strict or weak), since they seem to be less prominent than 2-categories. I would suggest the merger (to higher category theory for instance) —- Taku (talk) 06:51, 28 April 2025 (UTC)[reply]

I agree to merge. I think Tetracategory can be merged as well. But, a better target for redirection might be Weak n-category. Of course, it is possible to merge the weak n-category into the higher category theory.SilverMatsu (talk) 15:14, 28 April 2025 (UTC)[reply]

I’m not too sure if everything should be merged into “higher category theory”. It seems an n-category (weak or strict) deserves its own article. Certainly, higher category theory isn’t just about the study of n-categories. —- Taku (talk) 16:19, 28 April 2025 (UTC)[reply]

The coherence theorem for tricategory states that tricategory is triequivalent to Gray-category. So the strict version of tricategory seems to be Gray-category. Also, the coherence theorem does not seem to have been found for n>3. See https://mathoverflow.net/questions/334849/coherence-theorem-for-tetracategories-weak-n-categories and Lack, Stephen (2011). "A Quillen model structure for Gray-categories". Journal of K-Theory. 8 (2): 183–221. arXiv:1001.2366. doi:10.1017/is010008014jkt127.SilverMatsu (talk) 06:18, 29 April 2025 (UTC)[reply]

Thank you. So on second thought, maybe it makes sense to have an article on 3-category just as we have one on 2-category. I have already begun the draft Draft:3-category, where we can discuss Gray tensor product and such too. Taku (talk) 07:06, 29 April 2025 (UTC)[reply]

Speedy deletion nomination of Walks on ordinals

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A tag has been placed on Walks on ordinals requesting that it be speedily deleted from Wikipedia. This has been done under section G4 of the criteria for speedy deletion, because the page appears to be a repost of material that was previously deleted following a deletion discussion, at [[Special:PermanentLink/1268286608#Walks on ordinals]]. When a page has substantially identical content to that of a page deleted after a discussion, and any changes in the content do not address the reasons for which the material was previously deleted, it may be deleted at any time.

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The Japanese Red Cross Kyushu International College of Nursing moved to draftspace

Thanks for your contributions to The Japanese Red Cross Kyushu International College of Nursing. Unfortunately, I do not think it is ready for publishing at this time because of the discussion outcome at Wikipedia:Articles for deletion/The Japanese Red Cross Kyushu International College of Nursing. I have converted your article to a draft which you can improve, undisturbed for a while.

Please see more information at Help:Unreviewed new page. When the article is ready for publication, please click on the "Submit your draft for review!" button at the top of the page OR move the page back. Dclemens1971 (talk) 01:58, 28 April 2025 (UTC)[reply]

Higher category theory

Hello! First, thanks a lot for all your contributions to higher category theory! I already translated some of your articles into German in the past. I'm writing you because I just created seven new articles about higher category theory and noticed, after creating the one for the twisted diagonal, that you've already dead-linked it in one of your contributions. Since we're both active in the same area and both use Denis-Charles Cisinski's Homotopical Algebra as a source, I want to avoid any collisions. Therefore: I'm basically done with contributing to higher category theory in the English Wikipedia anyway and will soon go back to differential geometry or other different areas and also translating articles for the German Wikipedia, since both of us have written a lot to catch up to. The only articles I still plan to create are one for the Grothendieck–Segal condition and Homotopical Algebra itself, maybe also for proper/smooth and final/cofinal morphisms, but I still have to think about that. You can of course tell me, if you plan to do that as well. I don't plan to create the article Hom functor of an ∞-category, which I've dead-linked on twisted diagonal, since it fits more what you're writing and you're surely more qualified to do so.

Also, what do you think about an own article about anodyne extensions? I've thought about writing one for the German Wikipedia and then found out you've extended the notes in the English Wikipedia. Samuel Adrian Antz (talk) 06:47, 2 May 2025 (UTC)[reply]

Hi. I have definitely been noticing that you have added quite a few materials on higher category theory too (and I'm very flattered for being thanked). I am not really worried much about the collisions. After all, in Wikipedia, articles are supposed to be co-written by various editors (not much different from co-authored papers). Currently I don't have much a plan to add stuff from Cisinski's book. I'm more interested in stacks. As for the hom functor, a natural place for it is probably quasi-category. I'm not sure if we need a separate article for it. In Higher Topos Theory, Lurie actually gives a very simple quick construction using topology before stating the infinity-version of Yoneda's lemma. So, maybe that's the best approach (it seems Cisinski likes to avoid topology). For anodyne extensions, as you probably know, the notion also exists more generally than just for simplicial sets. So, maybe a standalone article on it may make sense. (I will probably not create one myself, though.) Another possibility is to put the topic in a standalone article on construction of model category structures or something. -- Taku (talk) 10:43, 2 May 2025 (UTC)[reply]

Merge proposal

Regarding the proposal to merge Coherence condition and Coherency (homotopy theory), where I removed the templates (and you reversed), it wasn't that the proposal had been open for too long, but rather that there was no case made, and the case isn't obvious. See WP:MERGEPROP Step 1. Would you mind making a case for the merge? Klbrain (talk) 14:43, 2 May 2025 (UTC)[reply]