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categories: Re: Categories ridiculously abstract



Readers of the cat list may be interested in the one meaningful post 
to Slate's "The Fray" in reply to Holt's MSRI "Diary" article. It was 
made  by David Yetter:

                                              
                                               category theory
                                               David Yetter
                                               28 Nov 2000 20:29


It is sad more than a decade on since the
proof of the remarkable categorical coherence
theorem of Shum that mathematicians can
continue to view category theory as a mere
linguistic convention or useless abstraction.

Shum's theorem shows that axioms
completely natural from the internal dynamic of
category theory completely characterize
framed tangles, relative versions of the framed
knots and links which are central to
smooth topology in 3 and 4 dimensions (notice
the dimensionality of space and of
space-time: hardly divorced from meaning.) Other
categories satisfying the same axioms
include the categories of representations of
quantum groups, physically motivated
algebraic structures which have become central
objects of study for mathematicians from
many old branches of mathematics.

Indeed, Shum's theorem, a theorem of
category theory, is the only really satisfying
explanation for the intimate connection
between quantum groups and low-dimensional
topology.