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## [Axiom-developer] categorial rep and per?

**From**: |
Ralf Hemmecke |

**Subject**: |
[Axiom-developer] categorial rep and per? |

**Date**: |
Sat, 12 May 2007 11:35:04 +0200 |

**User-agent**: |
Thunderbird 2.0.0.0 (X11/20070326) |

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