Subject: categories: Re: WHY ...CONCERNED? III

From: [email-masked]
Date: Sat, 01 Apr 2006 18:40:28 -0500

Jim,
Perhaps complacency is another form of preoccupation. Very often
topologists or geometers who want a functor category say things like "this
may not exist".
Of course that is slightly better than use of quotients or limits in
analysis without asking whether they exist, but in the 21st century such
waffling is unbecoming to mathematics, especially when, as I suggest, it
can be replaced by crisp algebra.
Bill

--On Saturday, April 1, 2006 10:01 AM -0500 jim stasheff
<[email-masked]> wrote:

> Who is so preoccupied?
> Folks I know usually use category theory without worring about size
> jim
>
> F W Lawvere wrote:
>> WHY ARE WE CONCERNED? III
>>
>> The second main misconception about category theory
>>
>> Part of the perception that category theory is "foundations" (in the
>> pejorative sense of being remote from applications and development) is
>> due to a preoccupation with huge size. Since such perceptions hold back
>> the learning of category theory, and hence facilitate its misuse as a
>> mystifying shield, they are among our concerns. We need to deal with the
>> size preoccupation head on.

[balance of quotation omitted...]