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Re: [Axiom-developer] categorical design

From: root
Subject: Re: [Axiom-developer] categorical design
Date: Thu, 9 Oct 2003 23:47:27 -0400


re: categorical redesign.

My view of this is to think of Axiom's mathematics as a general
graph rather than as a lattice with loops. Think of drawing the
whole of the algebra on the surface of a sphere. Picking one of 
several defined starting points (sets, categories) in the algebra 
would be like rotating the ball until the chosen point is at the
north pole. Everything else is defined in terms of that pole.
Choosing a new point would be like rotating the sphere to 
adjust it to the new "north pole" and everything in the graph
now flows from that point. A loop in the algebra goes all the
way around the sphere and you can choose any point in the loop
as fundamental. The choices I made to "break the loop" were

I'm not sure if the graph-mapped-onto-a-surface resonates with
you but that's how I think about it. (The surface need not be a
sphere, of course).


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