This edit needs analogous adjustments to those pointed out in another thread here.
I am out of energy for the moment. Please look into it. Generally, please try to keep in mind that nLab entries need to retain a minimum of logical consistency as you drop material into them that is copied from elsewhere.
]]>adding text from HoTT wiki.
Anonymous
]]>The entry fell short of really citing the following in full, so I have added it now:
Yoshiki Kinoshita, Nobuo Yoneda (1930-1996)
&
Saunders MacLane, The Yoneda Lemma,
Math. Japonica, 47, No. 1 (1998) 155-156
(pdf, also: posting to catlist in 1996)
Section “Necessity of naturality” sounded like there is nothing interesting going on if we look at the unnatural isomorphism of hom-sets. But this isn’t the case, already in the 60s a graph-theoretical and purely categorical facts of this form have been established. I’m adding the two earliest references.
Tomas Jakl
]]>Added a reference to
I added a link to Emily Riehl’s book “Category Theory in Context”. Chapter 2. Universal Properties, Representability, and the Yoneda Lemma. I treasure her exposition.
]]>Regarding the ubuntu package (#72): for me it only worked after I also installed “latex-cjk-japanese-wadalab”. This package is ’recommended’ by the package “latex-cjk-japanese” that Mike mentioned, but depending on your configuration recommended packages might not be automatically installed.
]]>Great, then I think the issue may after all be that the two symbols are too similar in Stix. I can verify that when back from holiday.
]]>Re #94: Yes, I see that too, in the “Rules” inspector tab. I don’t know why it doesn’t show the math
rules. But it does show them in the “Computed” tab. Also, when I uncheck the body font family rule (in “Rules”), body text changes, but not formulas.
I am still confused, Dmitri, because it would seem that the styling for body rather than math is being used, which seems unlikely, especially since Matt does not see this, and I have not previously observed it either when testing in Firefox.
]]>Re #91: This is correct, I misread it.
However, the rule
math {
font-family:dejavu math tex gyre,cambria math,stix two math!important;
font-size:19px
}
in nlab.css somehow does not apply anyway, and the rule that I pointed above applies instead.
This is revealed by Firefox’s inspection tools.
]]>Firefox. W3Schools said Firefox has supported @media since 3.5.
I’m no web dev hotshot, but I wonder if Dmitri misread nlab.css. (Or maybe it’s been changed already?) Here’s the part using @media:
@media only screen and (max-width:960px){ .navigation:not(.navfoot){top:60px} h1#pageName{margin-top:100px} }
So it doesn’t look like this should affect loading or use of STIX.
]]>I actually do not know anything about this @media gadget! Of course I will look it up, but respecting it might be browser dependent. Which browser were you using, Matt? I think when experimenting in the past I have always got the Stix fonts as well.
]]>Thanks very much! Good catch regarding max width, that seems like it would explain it. I’ll investigate that when back from holiday.
]]>Here is what Firefox shows for the first displayed formula in the Yoneda lemma article as the applied CSS style:
body { font-family: “dejavu serif”,cambria,Serif !important; }
This comes from the beginning of the nlab.css file.
So if DejaVu Sans or Cambria are installed, they will be used, otherwise, the generic serif font will be used.
The style specified for the math element, which includes STIX fonts, simply does not apply here, because it specifies @media max-width: 960px, but my screen width is 3840 pixels.
]]>Re #84: That should not be possible for displayed mathematics. The embedded Stix font should be used if the other two are not found. If you see other behaviour, please post a screenshot from something like F12 in Chromium which shows which font is used.
]]>Most mathematicians (except mostly native readers) don’t know hiragana.
Sure, they don’t. Perhaps because they are never exposed to it :-)
Mathematical notation is one of my pet-peeves (those of you who know me in person, or worse, those of you who read one of my papers, might have noticed it…), but with the passing of time this idiosyncrasy acquired a deeper meaning.
We name things so that they can be distinguished: I see no point in trying to economize in this respect, as if names were subject to exhaustion. But it is even more a nuisance that mathematical symbols are very often overloaded with meaning (“normal”, “nice”, “admissible”, “good”, …). However, that’s not my point here.
I chose to use the hiragana よ for the Yoneda embedding essentially because there was a precedent in this respect, but all the more because Yoneda was Japanese. But there’s a deeper reason behind this and similar choices.[¹]
Do you ever wonder, in doing Mathematics, to what extent the ideology that permeates it (like in every other product of the human intellect, Mathematics has an ideology) is centered in Latin/Germanic cultures? I often do, and at the same time I wonder what I can do to balance this trend. Human culture is wide and rich: we have built a word for basically any concept, provided we search far enough from our home culture.
Thus, to me, using Georgian, cuneiform, hiragana, Hebrew and Sanskrit alphabets is a precise “political” choice (that’s a heavy word, I guess, but I can’t find a better one): when I need to denote something exotic, or when I need syntax to convey a certain “flavour” together with semantics, I sometimes find restrictive to limit to Latin and Greek alphabet.
Maybe, notation is a different matter, but I feel I’m not the only one having this peculiar ésprit, especially among category theorists :-) when we study topos theory, we sketch an elephant and not a squid, because of an old Jain tale about five (four? six?) blind men touching an animal (=a category) that resembles a tree, a throne, a fan… according to the side where you approach it from. So are toposes! You can only grasp their true nature if you approach them from every side at once. And the methaphor is borrowed from Indian culture, because Western philosophy doesn’t contain a concept similar to Jain anekanta (more or less, “manifoldness of thought”).
===
[¹] See e.g. recollements or yosegi.
]]>No, the problem was that if a user does not have DejaVu Sans or Cambria installed, then formulas will use whatever sans serif font is installed, which need not distinguish between esh and integral.
Concerning STIX: I suggest that we switch to the improved XITS fonts: https://en.wikipedia.org/wiki/XITS_font_project
]]>The Stix fonts are embedded for exactly this reason, to serve as a backup. Is the problem that the two symbols look the same in Stix? Should we embed something else?
]]>I do have DejaVu fonts installed now, but this was a separate step that I had to do, and a lot of Linux users don’t have them installed.
]]>Are you saying you don’t have those fonts available and that’s why they don’t look different for you?
]]>