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.h...
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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