Re: Categories and functors, query

[jim stasheff <jds@math.upenn.edu>]

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.