Re: How to visualize limits in category theory
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Date: 12/19/04
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Date: 18 Dec 2004 17:29:20 -0800
Oh come on, just admit it! You're thinking in terms of venn diagrams
like the rest of us ;)
KRamsay wrote:
> 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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