evil

[John Baez <baez@math.ucr.edu>]

Sorry, if it's not too late please post this one instead:

From: John Baez <baez@math.ucr.edu>
Date: Tue, Sep 14, 2010 at 3:33 PM
Subject: Evil
To: categories <categories@mta.ca>


David wrote:

Jean Benabou wrote:
>> Maybe my english isn't so "beautiful", but in all cases where "evil" has
>> been used, what is wrong with "wrong" instead?
>

I'm not so enamoured with the use of the word 'evil', but it seems to
> be more entrenched than perhaps it was intended, namely as a joke.
>

It's supposed to be funny, but I'm glad to see it become entrenched.

Why?

First, it has a very specific meaning.  A property of objects of some
category C is said to be "evil" if it holds for some object x of C but not
some isomorphic object y.  More generally: a property of objects of some
n-category is "evil" if it holds for some object x but not some equivalent
object y.  For details, see:

http://ncatlab.org/nlab/show/evil

Second, it captures the interesting state of affairs in category theory
where some definitions can be well-formed yet somehow "suboptimal" because
equations were used when isomorphisms should have been specified.

"Wrong" doesn't work here, since mathematicians use it in other important
ways: for example, "false", "incorrect" or "inappropriate".  "Evil" is, to
the best of my knowledge, never used in mathematics except in this one
technical sense.

If anybody finds the term "evil" upsettingly strong, I suggest "naughty" as
an alternative.

Best,
jb


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]