categories: Lie groups and Lie algebras

categories: Lie groups and Lie algebras

[Tim Porter]

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Reply-To: Tim Porter <t.porter@bangor.ac.uk>

In the relationship between Lie groups and Lie algebras, there is the
neat result that the Lie functor L : LieGrp->LieAlg restricts to an
equivalence on the simply connected Lie groups, and that the fibre
over any given Lie algebra is the category of those G which are
isomorphic to quotients of the one simply connected one of them and
hence there is a Galois theory interpretation in terms of central
extensions.

I am sure that this sort of situation must be much more general than
just this case, and is somehow linked to abstract Galois theories. I
am hoping that someone can point out really neat categorical results
on this (in the literature).  I am sure I ought to know them but ...

It does not seem to be in Borceux-Janelidze, and my own library on
this area is very sadly thin on the ground.


Thanks in advance,

Tim



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