The lie algebra functor $T_1$ takes a Lie group to its lie algebra. I figure that this functor should be representable, since $T_1 \cong\mathrm{Hom}_{\mathbf{LieGrp}}(\mathbf{R},-)$. Is this true?
2026-04-25 03:14:56.1777086896
Representability of the Lie algebra functor.
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Yes, although I don't know why you'd call it the Lie group functor as opposed to the Lie algebra functor.