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categories: Re: Categories ridiculously abstract



I don't think one should blame the guy whose remarks Peter quoted.  He is
not a mathematician and presumably knows nothing more than some college
level mathematics.  He has picked up that attitude from the high-powered
mathematicians that inhabit places like MSRI (and the CRM, Fields Inst.,
and PIMS in Canada).  Ignoring the fact that category theory was fathered
by two of the most eminent mathematicians of the last century and
god-fathered by arguably the very greatest, they still go around saying
that it is without content and nothing but meaningless abstraction.  I was
unaware of what David Yetter mentioned, but I am certainly aware of the
crucial role categories had in proving the Weil conjectures and the fact
that people like John Baez seem to believe that higher dimensional
categories will be important in physics.  I might also point out that
categories were the right framework for Kaplansky's very elegant proof of
the Auslander-Buchsbaum theorem.  And here is a question: are categories
more abstract or less abstract than sets?

Michael