Re: The disdain for categories

Re: The disdain for categories

[jim stasheff]

Andre Joyal wrote:
> Jim Stasheff wrote:
>
>   
>> In my experience, disdain for cat theory is due to papers with a very
>> high density of unfamiliar names
>> reminiscent of the minutia of PST and the (in) famous comment (by some
>> one) about something like:
>> hereditary hemi-demi-semigroups with chain condition
>>     
>
> The chosen example is not too convincing, 
> since the notions involved are not typically categorical.
> Complicated sentences like this can be found in every fields.
> They are often the mark of a poor paper.
> Category theory is a powerful tool for crossing 
> the boundaries between the fields.
> The unity of mathematics is growing stronger every day.
>
> andre
>
>   

Indeed, the quote I was misremembering was NOT in category theory
how's that for crossing the boundaries between the fields. ;-)
in fact, it turns out that the correct usage is
hemi-demi-semi-quaver - in music!

jim

> -------- Message d'origine--------
> De: cat-dist@mta.ca de la part de jim stasheff
> Date: mar. 09/09/2008 18:22
> À: categories@mta.ca
> Objet : categories: Re: Categories and functors, query
>  
> Walter,
>
> I beg to differ only with
>
> In my experience, skepticism towards category theory is often rooted in
> the fear of the "illegitimately large" size, till today.
>
> In my experience, disdain for cat theory is due to papers with a very
> high density of unfamiliar names
> reminiscent of the minutia of PST and the (in) famous comment (by some
> one) about something like:
> hereditary hemi-demi-semigroups with chain condition
>
> jim
>  Tholen wrote:
>   
>> There is another aspect to the E-M achievement that I stressed in my
>> CT06 talk for the Eilenberg - Mac Lane Session at White Point. Given the
>> extent to which 20th-century mathematics was entrenched in set theory,
>> it was a tremendous psychological step to put structure on "classes" and
>> to dare regarding these (perceived) monsters as objects that one could
>> study just as one would study individual groups or topological spaces.
>> In my experience, skepticism towards category theory is often rooted in
>> the fear of the "illegitimately large" size, till today. By comparison,
>> Brandt groupoids lived in the cozy and familiar small world, and their
>> definition was arrived at without having to leave the universe. With the
>> definition of category (and functor and natural transformation)
>> Eilenberg and Moore had to do a lot more than just repeating at the
>> monoid level what Brandt did at the group level! In my view their big
>> psychological step here is comparable to Cantor's daring to think that
>> there could be different levels of infinity.
>>
>> Cheers,
>> Walter.
>>     
>
>
>
>
>   

The disdain for categories

[Andre Joyal]

Jim Stasheff wrote:

>In my experience, disdain for cat theory is due to papers with a very
>high density of unfamiliar names
>reminiscent of the minutia of PST and the (in) famous comment (by some
>one) about something like:
>hereditary hemi-demi-semigroups with chain condition

The chosen example is not too convincing, 
since the notions involved are not typically categorical.
Complicated sentences like this can be found in every fields.
They are often the mark of a poor paper.

My guess is that the disdain for categories has a mixed origin.
Like logic, category theory has a taste for generalities.
But most mathematicians are specialised and they find
it hard to believe that important progresses can be made in their fields
from the outside, as the result of general insights.
But we all know that the division of mathematics into fields 
is justified more by sociology than by science. 
Category theory is a powerful tool for crossing 
the boundaries between the fields.
The unity of mathematics is growing stronger every day.

andre

-------- Message d'origine--------
De: cat-dist@mta.ca de la part de jim stasheff
Date: mar. 09/09/2008 18:22
À: categories@mta.ca
Objet : categories: Re: Categories and functors, query
 
Walter,

I beg to differ only with

In my experience, skepticism towards category theory is often rooted in
the fear of the "illegitimately large" size, till today.

In my experience, disdain for cat theory is due to papers with a very
high density of unfamiliar names
reminiscent of the minutia of PST and the (in) famous comment (by some
one) about something like:
hereditary hemi-demi-semigroups with chain condition

jim
 Tholen wrote:
> There is another aspect to the E-M achievement that I stressed in my
> CT06 talk for the Eilenberg - Mac Lane Session at White Point. Given the
> extent to which 20th-century mathematics was entrenched in set theory,
> it was a tremendous psychological step to put structure on "classes" and
> to dare regarding these (perceived) monsters as objects that one could
> study just as one would study individual groups or topological spaces.
> In my experience, skepticism towards category theory is often rooted in
> the fear of the "illegitimately large" size, till today. By comparison,
> Brandt groupoids lived in the cozy and familiar small world, and their
> definition was arrived at without having to leave the universe. With the
> definition of category (and functor and natural transformation)
> Eilenberg and Moore had to do a lot more than just repeating at the
> monoid level what Brandt did at the group level! In my view their big
> psychological step here is comparable to Cantor's daring to think that
> there could be different levels of infinity.
>
> Cheers,
> Walter.