Re: A well kept secret?

["Joyal, André" <joyal.andre@uqam.ca>]

John Baez wrote:

>They fought to convince the world that category theory was
>worthwhile. Some feel they lost that fight.  We came along later and
>are a bit puzzled by that attitude: if you look around at the
>landscape of mathematics today, categories are everywhere!  From
>Grothendieck to Voevodsky to Lurie, etc., much of the most exciting
>mathematics of our era would be inconceivable without categories.

Like most fields of mathematics, category theory keeps growing and evolving. 
It may be hard to identify the mechanism of this evolution 
but fashion must be playing a role.
But why are certain subjects becoming hot at a given time?
Probably because they resonate with new developments outside category theory.
When a trend becomes hot, it gives rise to a permanent current. 
I was able to distinguish approximatly 6 major currents:

1) Algebraic topology and homological algebra

2) Abelian categories

3) Algebraic Geometry and topos theory 

4) Logic and elementary topos theory

5) Category theory and computer science

6) Higher categories with homotopy theory  

Here is an example of a recent applications of category theory to geometry:

"Associahedral categories, particles and Morse functor" 
by Jean-Yves Welschinger http://arxiv.org/abs/0906.4712 

The n-category caffé is an extraordinary experiment in 
research collaboration and dissimination of knowledge.
It maybe the way of the future.
But an old mathematicians like me find it 
difficult to adapt to this new form of collaboration. 

>The only real question is whether our current civilization, based on burning
>carbon, tearing up forests, and destroying oceans, lasts long enough to see
>this change.

Yep! And we should not remain passive.

Best,
AJ



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