Re: are fibrations evil?

[Toby Bartels <toby+categories@ugcs.caltech.edu>]

Eduardo J. Dubuc wrote:

>Furthermore, the introduction of new terminology (specially if this
>terminology refers directly to a meaning in everyday life) with no real
>need and/or to change established terminology, is an habit that harm the
>credibility of any school of research.

Shall we stop saying "natural" and say "invariant under composition"?
Or is that term allowed under the grandfather clause,
since it was being used imprecisely before category theory defined it?
If I can find a citation where John Baez used the term "evil"
before he knew how to define it, will that make it OK?
Or is that irrelevant because John was already working in the ghetto?

>In the present case we are discussing a particular single word "x" to
>replace the compound "not invariant under equivalence". This seems
>justified by its frequent use, but its frequent use is due precisely
>because we are discussing its use !!!.

As a proud citizen of the Ghetto of Category Land,
I've used that term in other contexts than this discussion.
If you do not wish to join us, what does that matter?
You may continue to write down strict definitions,
and we will continue to weaken them as we need.
Different styles of mathematics are not at war.

I understand that "evil" is grating; other terms have been suggested.
But no, *any* short term to replace "not invariant under equivalence"
is forbidden by your decree: it relegates us to the ghetto.
Well, that is your interpretation, but it doesn't affect my mathematics.


--Toby


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