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I have re-typeset the “periodic table” (here), now in our Instiki/markdown syntax instead of html (and re-including the dollar signs).
I have just blindly re-produced the entries of the table as it was, but I have myself not thought about $A_n$-stuff for $n \lt \infty$ and I don’t fully follow what the entry is saying: It seems from the last row that the claim is that there is first a stabilization at large finite $k$ and then again a jump as one goes to the limit $k \to \infty$??
I only now fully realize that this entry and most of the pages it links to were created and solely authored by Anonymous activity in summer 2022.
All these entries (like A4-spatial groupoid) contain neither definitions nor references. While at first glance they seem too trivial to have any issues, something seems amiss and something seems wrong with that table. (Was this on the HoTT wiki?)
If anyone would like to vouch for these entries and help try to improve them that would be good. Otherwise it might be that we should delete them.
Just to bump this up again: Does anyone see value in this entry and sees themselves working to improve it?
The name “A4-spatial groupoid” seems wrong in any case: it should be just an $A_4$-space or perhaps an $A_4$-groupoid, and as such is redundant with An-space.
Thanks for the feedback. And wouldn’t an $A_4$-groupoid just be a monoidal groupoid? That would solve the problem with the systematics of the table.
I haven’t unwound the definitions to carefully check the stabilization degree (for the time being I am looking into this not out of interest into the subject, but just as an editor trying to steer the nLab), but I think this must be true. So I have replaced now in the table the entry “A4-spatial groupoid” with “monoidal groupoid” and “A5 spatial 2-groupoid” with “monoidal 2-groupoid”. This way the table now finally seems to make sense in itself.
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