Meaning of U+22B6 and possible mistakes

[Marius Spix]

It seems that the symbol U+22B6 has been used first by Joachim Kock
from UAB Barcelona Maths Department. He is also using on a website, last
modified in 2006, four years before the already mentioned paper
“Polynomial functors and opetopes” had been published.[1]

The symbol has been “borrowed” from other authors, e. g. [2], [3]

Maybe Mr. Kock can provide more information about the origin of that
character and also answer the other questions. 

[1] https://mat.uab.cat/~kock/cat/zoom/examples.html
[2]
http://www.lix.polytechnique.fr/Labo/Samuel.Mimram/docs/mimram_optt.pdf
[3] https://github.com/ggreif/seminar-opetope (with diamonds instead of
circles, though)


On Fr, 3 Sep 2021 18:07:14 +0200
Ivan Panchenko via Unicode <unicode at corp.unicode.org> wrote:

> Consider the following character names:
> 
> ORIGINAL OF (⊶, U+22B6)
> IMAGE OF (⊷, U+22B7)
> 
> I find “original” as a noun strange in this context. How about
> “origin”, “domain” or “source”? However, the only mathematical use of
> “⊶” that I found was in the context of zooms as defined in section
> 1.5 here: https://arxiv.org/pdf/0706.1033.pdf
> 
> This work is from 2010, but the character already existed in Unicode
> 1.0.0, so I am not sure what it was supposed to mean after all. Any
> hint? Perhaps U+2290 ⊐ SQUARE ORIGINAL OF was supposed to have the
> same meaning as U+22B6 (why else would it be named this way?).
> 
> Furthermore:
> 
> SUBSET OF WITH NOT EQUAL TO (⊊, U+228A)
> LESS-THAN BUT NOT EQUAL TO (≨, U+2268)
> SQUARE ORIGINAL OF OR NOT EQUAL TO (⋥, U+22E5)
> 
> The first of these names employs the word “with” to describe how
> U+228A looks like, the second one employs the word “but” to describe
> what U+2268 means. (A bit inconsistent, but fine so far.)
> 
> In the third one, I find the “or not equal to” part strange. Would
> “BUT not equal to” not be more plausible?
> 
> Sidenote (not an issue with Unicode): I find it remarkable that while
> “≤” is used to mean ‘is less than OR equal to’, we use “⊊” for ‘is a
> subset of AND not equal to’, which breaks the analogy. I might prefer
> “⊊︀” (with stroke through bottom members) to “⊊” for this reason. The
> file bsymbols.mf of amsfonts deviously contains “cmchar "Subset or
> not equal to sign"”. Cf. Paul Taylor for a criticism of the use of
> “⊂” for the proper subset relation:
> https://books.google.com/books?id=iSCqyNgzamcC&pg=PA75&q=%22but+strict+inclusion+is+neither+primitive%22
> Schröder (1890) actually used a symbol (in the strict sense) that
> looked similar to our “⊂” but went up- and downwards like the
> less-than sign; I do not advocate reintroducing it either since we
> also write “∩” and “∪” (analogously to “∧” and “∨”) with parallel
> lines.