Re: How to visualize limits in category theory

From: KRamsay (kramsay_at_aol.com)
Date: 12/19/04 

Date: 19 Dec 2004 01:09:27 GMT

In article <cpun6f$oji$1@panix5.panix.com>, lrudolph@panix.com (Lee Rudolph)
writes:
|"Jesse F. Hughes" <jesse@phiwumbda.org> writes:
|>barr@barrs.org (Michael Barr) writes:
|>
|>> When I think about limits, I think about subobjects of products.
|>
|>That's *much* clearer than what I wrote, when I said a category is
|>complete just in case it has equalizers and products. My answer is
|>relevant to completeness, but not a good answer to how to visualize
|>limits.
|
|I was pleased to see Michael Barr rework the verb being used
|into "think about", and I'm distressed to see you return to
|"visualize".

When I visualize products, I often visualize them as boxes. When
I visualize subobjects, I often visualize them as amorphous shapes
inside the boxes. :-)

Actually, I tend to keep a picture in mind of the diagram used to
define the limit object, picturing the object itself as the result of
a compromise between two forces. The definition can be considered
in two parts; on the one hand the object has to be large enough
(it has supporting struts inside...) and on the other hand it can't
be excessively big (it has a tight covering surrounding it).

Keith Ramsay

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