Alain Connes on Toposes and Integers

From Toposes in Como, 2018. Alain Connes was a part of Nicolas Bourbaki.


A really smart kid would say that you only need to learn exponentiation, then you already know how to multiply and add, because you can compose exponentials, so you know that (a^x)^y=a^(x*y) and (a^x)*(a^y)=a^(x+y). I did this once with a higher-order functor in Moscow ML. The result was a lamba expression with three curried arguments that did all three arithmetic operations. I am still trying to understand what a Cartesian Closed Category is though, ...

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