Timelines for category theory: a response to comments

[Ronnie Brown <ronnie.profbrown@btinternet.com>]

Dear Colleagues,

Many thanks for your comments, which show how our community sees the
problem. The discussion is obviously not finished yet.

Let us actually try to say what is the MAIN problem with this article.
The main problem is the picture of category theory it draws! Many of you
give courses in category theory at various levels - beautiful courses
showing that category theory provides a new most advanced level of
thinking in mathematics ("thinking categorically!"), and has made major
contributions to the unity of mathematics. So, why don't you compare the
plan of your own course with this article? Surely you do not begin your
course with resolutions of modules and you do not end it with "extended
TQFT", do you?

On the other hand there is clearly a desire to have a good content  and
context for category theory on wikipedia, which is often the first port
of call for students, and those potentially interested, and so there are
calls for an improved Timeline for category theory. To take in the whole
subject in one timeline, with references, would seem an enormous and
controversial task.

We therefore propose that the present article be replaced by  a list of
topics with links to articles on timelines of those topics. And then
each "timeline" should be written by a chosen group of experts. 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

There will be intersections of course, but we presume that is fine.

As examples of timelines in other subjects, and their styles, see for
example

http://en.wikipedia.org/wiki/List_of_timelines#Science

particularly those on Physics.

We look forward to reactions to this proposal.

Ronnie Brown

George Janelidze


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