Re: Timelines for category theory: a response to comments

[Graham White <graham@eecs.qmul.ac.uk>]

I think, judging by comments so far, that there are basically two
goals concealed within "this project". One is to write an outline of
category theory as it seems to us now; the other is to write a history
of category theory, and, specifically, a history of who influenced whom.
Both of these are very worth doing, but the second is much more
difficult.

It's difficult mainly because it entails recovering a consistent history
from people's reminiscences, and these will not be consistent with
each other: they will be inconsistent not just because people's memories
are not accurate, but because everyone has remained active in the field
and they alter their memories according to what they think now. This is
probably especially true of mathematicians, because mathematicians
always rephrase other people's stuff in their own terms: it's how they
come to understand it. (Remember Goethe's remark, "Mathematicians are
like Frenchmen: if you tell them something, they rephrase it in their
own language, and you cannot understand it any more"? Well,
mathematicians do that to each other as well as to non-mathematicians).

The history is hard to do, but also potentially very valuable: it would
show how a revolution in mathematics took place. Hard work, though.

And *not* in the form of a Wiki, because Wikis deal with contradictions
between documents by erasing one document in favour of the other. (I
know, you can always look back in edit history, but it still relegates
one of the testimonies to the sidelines: you might well be in a
situation where you just have more than one testimony, and where it
would not be sensible to prefer one to the other).

Graham

On Tue, Jul 12, 2011 at 06:48:53AM +0930, David Roberts wrote:
> Hi Ronnie,
>
>> ....Our first draft of topics would be:
>>
>> 1. General category theory, including motivation
>> 2. Abelian categories and homological algebra
>> 3. Categories and groupoids in homotopical algebra and algebraic topology
>> 4. Topos theory
>> 5. Monoidal, enriched, and higher-dimensional categories
>> 6. Categorical algebra
>> 7. Categorical topology
>> 8. Categorical logic and foundation of mathematics
>> 10. Categories in algebraic geometry
>> 11. Categories in computer science
>> 12. Categories in Physics
>
>
> a good candidate for what your 12., combined with 11., 8. and a bit of 5.  might
> look like is Baez and Stay's 'Rosetta stone' paper, see:
>
> http://golem.ph.utexas.edu/category/2008/03/physics_topology_logic_and_com.html
>
> Clearly this is only a tiny slice of the category theory cake, and perhaps again
> a biased one, but at least it contains facts, and references.
>
> Best of luck with this project, I look forward to contributing in what small way
> I can.
>
> David
>

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