Re: The boringness of the dual of exponential

[David Leduc <david.leduc6@googlemail.com>]

On Mon, Nov 7, 2011 at 07:59, Ross Street <ross.street@mq.edu.au> wrote:
> The conjecture is false.
> Take any category E where exponentiable is interesting.
> Then the dual of exponentiable is not boring in E^op.

Indeed! And this is clearly true of the example given by Thomas, namely Set^op.

However, I am not yet satisfied. Let me precise my thoughts. In the
textbooks and lecture notes on category category that I have read,
there are always product and coproduct, pullback and pushout,
equalizer and coequalizer, monomorphism and epimorphism, and so on.
However exponential is always left alone. That is why I assumed it is
boring. If it is not boring, why is it never mentioned in textbooks
and lecture notes on category theory?

Also, in logic, "and" goes in pair with "or", "for all" goes in pair
with "there exists". But implication is always left alone. Why is it
so?
Is it not the case in "dialectical logic" mentioned by Thomas? By the
way, I'd love to have some reference on models of dialectical logic.


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