Re: Bourbaki and Categories

[mjhealy@ece.unm.edu]

Andre Joyal's message was inspiring.  I think a new Bourbaki type of
effort (this time with motivation and category theory) is called for.  I
would like a text on categorical algebra oriented toward those who have
studied algebra and know enough category theory to use adjunctions, monads
and the like.  The same goes for categorical logic and model theory.

I read Andre's closing remarks as a commentary on the emerging crisis in
overcoming misconceptions about and outright hostility toward science and
mathemtics.  I have a current project, using my own meager funds and time,
to advance science teaching using a book available through the National
Academies Press, "Science, Evolution, and Creationism".  From the title, I
think you can see my motivation.

In a similar (although less aprocryphal) vein, when I worked with computer
scientists and applied mathematicians in industry ( and also when I've
submitted papers to certain neural network journals) I encountered
misconceptions about and outright hostility toward category theory.  For
example, in the dynamic systems community there seems to be a widespread
myth that "category theory was tried and failed".  I have followed this up
to some extent and haven't found any basis for it.  I am often told that
the best way to counter skepticism is with a working application.

Having tried that, and tried again, I've come to the conclusion that Yes,
you need applications, but applications cannot by themselves counter a
refusal to give a theory credit for being consistent with the data.  You
need a good, clear presentation of the theory couched in a language
oriented toward the intended audience.  As with biology teaching that
shows clearly the importance of the theory of evolution, maybe mathematics
teaching that incorporates category theory needs to begin in 6th Grade (in
schools in the USA) if not sooner.  Maybe a new Bourbaki project could
have an extension into this level of instruction.

Best Regards,
Mike


Please excuse my deviating from mathematics