> Of
> course this would only be after it has been broken up into connected
> components. Perhaps I'm over simplifying things...

If I understand it right, Nicolas suggested to move that stuff the the
CoxeterGroups category. In this generality, this approach of checking
finite types doesn't work, but the other way round should be possible
by checking if the Cartan matrix is a finite type Cartan matrix.

Cheers, Christian

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