Subject: categories: Categories - too abstract?

From: [email-masked]
Date: Thu, 30 Nov 2000 15:41:01 -0800 (PST)

Michael Barr write:
 
> 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. 

When I am confronted with this attitude, I sometimes use a couple of 
arguments in addition to the usual one of listing things that category 
theory is good for.  I present them here in a rather blunt form; they 
can be toned down as politeness dictates.

1) "You say category theory is `too abstract'.  But if you don't like
abstraction, why in the world are you doing mathematics?  Maybe you 
should be in finance, where the numbers all have dollar signs in front
of them.  Complaining that a piece of mathematics is `too abstract' 
is a bit like saying that the ocean is `too wet'."  

2) "You say category theory is `too abstract'.  Good!  Don't learn it!
That way, I'll make progress in my research faster than you." 

> And here is a question: are categories more abstract or less abstract 
> than sets?

Indeed, what we often take as "greater abstraction" is really 
unfamiliarity.  The real answer to the problem of people thinking
categories are "too abstract" is to keep explaining category theory
and how it's useful in a wide variety of problems... until people 
get used to it.   Physicists used to think groups were too abstract!

John Baez