Re: Bourbaki and Categories

[Vaughan Pratt <pratt@cs.stanford.edu>]

Bourbaki redone as Bourwiki (thanks, Dusko!) with the benefit of
category theoretic insights will hopefully clarify some segments of
mathematics.

What troubles me in this discussion however is its assumed scope of
"some."  I get the sense that there are people who want it to be
mandated as "all."

Perhaps it should be.

Just now I looked through an issue of American Mathematical Monthly that
came to hand to get a sense of the likely alignment of Bourwiki with
what the mathematical community generally regards as the scope of its
subject.  Actually I do this periodically, and I don't see much change
between the issue I picked up just now and any of the other issues I've
looked at in the past with just this question in mind.

If the subject Bourwiki is proposing to serve is mathematics, then
perhaps it is time that the American Mathematical Monthly, along with
the Putnam Mathematical Competition, the International Mathematics
Olympiad, and the Journal of the AMS, abandon their pretense of being
about mathematics and come up with a suitable name for their subject.
Not only do categories, functors, natural transformations, adjunctions,
and monads go unused in these 20th century icons of mathematics, they go
unacknowledged.  Clearly they have not gotten with the modern
mathematical program and fall somewhere between a throwback to a golden
age and a backwater of mathematics.  When they die off like the
dinosaurs they are, real mathematics will be able to advance unfettered
into the 21st century and beyond.

Judging from the talks at BLAST in Denver last month (B = Boolean
algebras, L = lattices, A = (universal) algebra, S = set theory, T =
topology), at least the algebraic community is moving very slightly in
this direction.  Things will hopefully improve yet further when
algebraic geometry gets over its snit with equational model theory.

Meanwhile if you need a witness for seven degrees of separation, look no
further than AMM and CT.

(I confess to being an unreconstructed graph theorist and algebraist
myself.  I may have to preemptively volunteer myself for re-education
before it becomes involuntary.)

Vaughan Pratt