FOM: Re: Picturing categorical set theory

[Colin McLarty]

Friedman writes:

        On category theory

>As technical mathematics, some of it, in moderate doses only,
>has limited and respected uses - it helps with the formulation of
>appropriate generalizations, and cleans up some proofs.

        As technical mathematics Grothendieck's ideas of Abelian categories
and derived functor cohomology were the inspiration for (and still
indispensable to) four Fields medals: Grothendieck, Atiyah, Deligne,
Faltings. They are central to the Langlands program--whose highest goal is
to prove the "functoriality principle"--and indispensable to Wiles's proof
of the Fermat theorem. As to the "moderation" of the doses, look into
Hartshorne's ALGEBRAIC GEOMETRY, and notice he *resists* categorical methods
as far as possible.

        If you think all mainstream mathematics is respectable only in
"limited doses" then you can agree with Friedman's claim. But don't think
category theory is a small part of the stream.

Colin