Re: are fibrations evil?

["Eduardo J. Dubuc" <edubuc@dm.uba.ar>]

Toby Bartels wrote:

>
> 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?

Dear Toby, your choice of example is very unfortunate. Mac Lane wrote that
category theory was invented to define functor, and that functor was invented
to define "natural" transformation.

How do you compare the importance of the concepts "invariant under
composition" (assuming that is the definition of "natural") and "invariant
under equivalence".

The discovery of the property underneath many important mathematical
developments (property not clearly evident or identified at the time) (like
Stone duality just one example) was an extraordinary accomplishment.

Invariant under equivalence is obviously used, is a concept already there
(whether true or false). The introduction of a new name for it can only be
justified by a frequent use, which is not clear at the moment.


> 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?

?????????????

   > 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.

Sorry, I never said that i will only write strict definitions (as a matter of
fact I have already written several non strict ones when I need them and they
were naturally the correct ones over the strict version).

If I run into a concept (or definition) non invariant under equivalence, I
will just say so. No need to introduce a name for it, and much worse to call
it "evil". Understand ?

> 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.

Your mathematics will not change a bit whether you use the term "evil", or any
other term "x", or simply "not invariant under equivalence".

e.d.



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