🚀 go-pugleaf

I had one or two questions to add to Adler ones, perhaps
some naughty cathegorist there can answer easily.

First, is the category of conmutative C*-algebras a topos?
Being as it is the dual (or it was the antiequivalente?) of the
category of compact topological spaces, it would be a  topos or sort of, am I
correct?

Second, what about the category of all C* algebras, this is, including the no
conmmutative algebras? Following Connes, you can use ANY C* algebra to make
diferential geometry. And you have "points" and "arcs" (R-->M or dually
C(M)-->R). This would have a categorial counterpart.

Third, which is the difference  from the categorial point of view of the two
categories? This would be: Which is the correct categorial formulation of
conmuttativity? But I m not sure if there are more diffs.

I dont know if categorists are or not in the side of Connes but I think they
would have something to say about all this stuff of non conmutative geometry,
manifolds etc...

Alejandro Rivero
rivero@cc.unizar.es