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October 26

Yoneda lemma (Continuation of Wikipedia:Reference desk/Archives/Mathematics/2026 October 7)

I'm still looking for the minimal condition (structure) under which the Yoneda lemma hold. So, even though it's not finished yet, but I created a table. (Does the user space allow pages like this one?) It seems there is no problem with the composition was partial and weakening the definition of associative that up to a coherent n-isomorphism or up to (coherent) homotopy when formulating the lemma, but when is not guaranteed, the formalization fails. When I was reading the 2-Yoneda lemma#∞-Yoneda, and I remembered that a quasi-category is a simplicial set, so I searched for "Yoneda lemma for simplicial set". Then I found a paper titled "The Yoneda Lemma for Simplicial Spaces". Should I add this to 2-yoneda?--SilverMatsu (talk) 02:20, 26 October 2026 (UTC)

A prerequisite for the Yoneda lemma to make sense in some playground of structures is that the notion of natural transformation makes sense there. So it makes sense to start with investigating that.
You can put anything on your user pages that is intended to improve the encyclopedic content on Wikipedia (and does not violate policies such as WP:ATTACK, WP:BLPTALK and WP:CIV that also apply to user space).  ​‑‑Lambiam 08:34, 26 October 2026 (UTC)
Thank you. I'll look into whether natural transformations make sense in each of these structures.--SilverMatsu (talk) 15:46, 27 October 2026 (UTC)

October 28

Surface Evolver in nonEuclidean space

I have played some with Surface Evolver and now I want to minimize some surfaces in 𝕊³. I asked Ken Brakke about doing it in stereographic projection and he said, yes you can do that, you just need to define a metric tensor. Ignorant of tensors, and not finding anything relevant in the documentation, I did not pursue the matter.

So I'm hoping to find and quiz someone who has used Evolver in non-𝔼 space. I asked Henry Segerman because he seemed likely to at least have a lead; he referred me to someone who did not reply, boo hoo. —Antonissimo (talk) 19:46, 28 October 2026 (UTC)

October 31