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Date:         Tue, 20 May 2014 22:00:39 -0700
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From: William F Hammond <gellmu@GMAIL.COM>
Subject: Re: Unicode math
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On Tue, May 20, 2014 at 2:34 PM, Chris Rowley <ca_rowley@yahoo.co.uk> wrote:

But more simply, I think of them as something like:
>
>     \mathoperator {\mathtext {\textbf {Var}}}
>

Yes.  Also when Var is 'R', I often prefer this to \mathbb{R} as an
'indicator' for the field of real numbers.  Yes, the word 'indicator' seems
to have first appeared chez MathML or perhaps chez OpenMath [it
can be hard to tell the difference :-) ]

I think the MathML distinction between 'indicator' and 'operator' has no
precise analogue in LaTeX.  Mathematically, in light of what the category
theorists have shown us, particularly as applied, for example, to what is
called the "functor of points" in algebraic geometry, one can think of
almost everything as a categorical "arrow".  To make this mundane, if x is
in n-dimensional space and f a map defined there, the notation fx  [ or
f(x) ]
can be regarded as a composition of arrows whether x is static or whether
it depends on some parameter t since a static x, i.e., a point, may be
canonically identified with the map from the one-point space to
n-dimensional space taking x as its value and likewise for f(x).  (To get
mathematical semantics out of this one just needs to understand the "type"
of each symbol.)

          -- Bill

-- 
William F Hammond
Email: gellmu@gmail.com
https://www.facebook.com/william.f.hammond
http://www.albany.edu/~hammond/

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<div dir=3D"ltr"><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">=
On Tue, May 20, 2014 at 2:34 PM, Chris Rowley <span dir=3D"ltr">&lt;<a href=
=3D"mailto:ca_rowley@yahoo.co.uk" target=3D"_blank">ca_rowley@yahoo.co.uk</=
a>&gt;</span> wrote:<br>
<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-lef=
t:1px #ccc solid;padding-left:1ex"><div id=3D":2lc" class=3D"a3s" style=3D"=
overflow:hidden">But more simply, I think of them as something like:<br>
<br>
=C2=A0 =C2=A0 \mathoperator {\mathtext {\textbf {Var}}}</div></blockquote><=
/div><br></div><div class=3D"gmail_extra">Yes.=C2=A0 Also when Var is &#39;=
R&#39;, I often prefer this to \mathbb{R} as an<br></div><div class=3D"gmai=
l_extra">&#39;indicator&#39; for the field of real numbers.=C2=A0 Yes, the =
word &#39;indicator&#39; seems<br>
</div><div class=3D"gmail_extra">to have first appeared chez MathML or perh=
aps chez OpenMath [it<br>can be hard to tell the difference :-) ]<br><br></=
div><div class=3D"gmail_extra">I think the MathML distinction between &#39;=
indicator&#39; and &#39;operator&#39; has no precise analogue in LaTeX.=C2=
=A0 Mathematically, in light of what the category<br>
</div><div class=3D"gmail_extra">theorists have shown us, particularly as a=
pplied, for example, to what is called the &quot;functor of points&quot; in=
 algebraic geometry, one can think of almost everything as a categorical &q=
uot;arrow&quot;.=C2=A0 To make this mundane, if x is in n-dimensional space=
 and f a map defined there, the notation fx=C2=A0 [ or f(x) ]<br>
</div><div class=3D"gmail_extra">can be regarded as a composition of arrows=
 whether x is static or whether it depends on some parameter t since a stat=
ic x, i.e., a point, may be canonically identified with the map from the on=
e-point space to n-dimensional space taking x as its value and likewise for=
 f(x).=C2=A0 (To get mathematical semantics out of this one just needs to u=
nderstand the &quot;type&quot; of each symbol.)<br>
</div><div class=3D"gmail_extra"><br></div><div class=3D"gmail_extra">=C2=
=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 -- Bill<br><br>-- <br><=
div dir=3D"ltr">William F Hammond<br>Email: <a href=3D"mailto:gellmu@gmail.=
com" target=3D"_blank">gellmu@gmail.com</a><br><a href=3D"https://www.faceb=
ook.com/william.f.hammond" target=3D"_blank">https://www.facebook.com/willi=
am.f.hammond</a><br>
<a href=3D"http://www.albany.edu/~hammond/" target=3D"_blank">http://www.al=
bany.edu/~hammond/</a><br><br></div>
</div></div>

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