[Axiom-developer] categorial rep and per?

[Ralf Hemmecke]

Hi Bill,

On

http://wiki.axiom-developer.org/SandBoxLimitsAndColimits

you write

> I am especially interested in how the duality between rep and per
> is involved in these constructions.

My answer is: I don't know.
And I also don't know why you think that per and rep is something 
categorial.

Suppose I have a domain R with some exports CatR. And I define for some 
other exports CatD a domain

D: CatD == add {
  Rep == R;
  ...
}

rep and per relate R with D (basically saying that they are the same 
things as data structures with no features). But their exports have no 
relation at all. Mathematically seen, they are objects of different 
categories. So rep and per would be functors (if anything). But how can 
such a construction be made functorial. I don't see that.

Ralf