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William F Hammond <[log in to unmask]>
Tue, 20 May 2014 22:00:39 -0700
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On Tue, May 20, 2014 at 2:34 PM, Chris Rowley <[log in to unmask]> 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: [log in to unmask]