At 18:27 +0900 98/10/15, Frank Christoph wrote:
>I encourage you to acquire some familiarity with a related field first, e.g.,
>universal algebra, topology or even type theory or logic, since category
>theory is very abstract stuff ("abstract nonsense" is a commonly cited
>description; of course, some people insist that category theory is more like
>the abstract nonsense _behind_ the abstract nonsense). Algebraic topology in
>particular _really_ puts category theory in perspective, as I learned
>recently.
I think perhaps algebraic geometry is an even better example, especially
Grothendieck's theories for handling the characteristic p case and other
such theories: For example, instead of just having a set theoretic
topology, one uses a Grothendieck topology defined in terms of category
theory, which can be used to define cohomology theories (such as derived
categories) on algebraic schemes. Abstractions of Grothendieck toposes led
to the concept of elementary toposes which can be used as a replacement for
set theoretic models. There is a lot of exiting spin-offs, such as using
derived categories to study singularities in analysis (D-modules) and
stratified manifolds in differential geometry. One can also mix these
theories with say QM (Quantum Mechanics) and GR (general relativity).
Very exiting stuff, but I should caution that there is a risk that the
person studying it will be diverted from the original programming tasks for
a period of time (like a couple of years).
Hans Aberg
* Email: Hans Aberg <mailto:[EMAIL PROTECTED]>
* Home Page: <http://www.matematik.su.se/~haberg/>
* AMS member listing: <http://www.ams.org/cml/>
