On Sep 20, 2008, at 8:47 AM, Rob Freeman wrote: (01)
> I would welcome comments on a possible relationship between gauge
> theories in physics, Category Theory in maths, and semantics.
> (02)
Well, you did ask. These three topics have absolutely nothing whatever
to do with one another. Gauge theories focus on symmetries in physical
theory: that is, ways in which theories are invariant under various
mathematical transformations. Category theory is a branch of pure
mathematics, a kind of ultimate abstraction of algebra, which focusses
on systems ('categories') defined by mappings . Semantics is concerned
with the relationship between representations and what it is that they
represent. One might as well ask for comments on a possible
relationship between botany, music and gardening. (03)
Let me ask in return, what was it that suggested to you that these
three topics might have any relationship? (04)
Pat (05)
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