Re: Bourbaki and Categories

["R Brown" <ronnie.profbrown@btinternet.com>]

There are already some pretty good categorical entries on wiki; I have
modified some of the entries on groups, actions, equivalence relations,  to
include references to groupoids, which has resulted in hits. But we should
also consider planetmath.org (entries are contributed under the terms of the
GNU Free Documentation License (FDL)) which allows for group work and is not
so open as wiki to general modification. It needs a group of you wonderful
energetic people to engage with reviewing what is on wiki and planetmath and
making sure they express what is fealt to be desirable!

In the old days, a graduate book would have an appendix on say set theory,
and maybe basic algebra, as needed for the rest of the text. It would be
very useful to have basic category theory (in terms of `the basic facts of
life') on the web available to all, with nice accounts of say `left adjoints
preserve colimits', etc. , with many convincing examples, and maybe history,
to which a text could refer. Something initially less ambitious like this
might actually get done. Being electronic, it would be  seen as a `current',
rather than `final account', and so would better reflect the way mathematics
develops, in which a slight shift of emphasis, or notation (like --> for a
function), can have profound consequences.

There is perhaps a  case for a separate collected electronic account, with
hyperref, and also a printed version, since a book is a useful portable
random access device. Print on Demand allows this to be produced quite
cheaply, with a 35% royalty on retail sales, and available on amazon.

Ronnie

----- Original Message -----
From: "Vaughan Pratt" <pratt@cs.stanford.edu>
To: <categories@mta.ca>
Sent: Tuesday, September 16, 2008 9:57 AM
Subject: categories: Re: Bourbaki and Categories


> 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
>
>