Subject: categories: Re: cracks and pots

From: David Yetter <[email-masked]>
Date: Wed, 29 Mar 2006 09:02:27 -0500

I used the word 'faces' to describe the two aspects of category theory. 
  I see no actual separation in content, only a difference in emphasis 
(esp. as regards applications) and public presentation.

Even as Saunders, late in his life, gave lectures entitled 'All 
Mathematics Belongs Together', so all category theory belongs together.

D. Y.

On 28 Mar 2006, at 03:01, dusko wrote:

> i think david yetter's analysis of the dichotomy "categories as 
> foundations" vs "categories as algebra" was spot on ---  with respect 
> to people and the community. indeed, one could split most of our 
> papers into one category or the other. 
>
> but at the end of the day, i think, we'll all agree that the source of 
> the unreasonable effectiveness of categorical algebra is its 
> foundational content (although there is probably a lot of it that we 
> dont understand yet); and the other way around. eg, if you look at 
> grothendieck's work, he started working in algebra, and ended up 
> developing foundational structures, because he needed them. and a lot 
[lengthy further quotation omitted ...]