Groups pop up as automorphism groups in any category.

Rings pop up as endomorphism rings in any additive category.

Is there a similar way to attach a Lie algebra to an object in a category of a certain sort? Maybe even such that the attachment of a Lie algebra to a Lie group becomes a special case?

And yes, I have searched through the answers to [Why study Lie algebras?](https://mathoverflow.net/questions/58696/why-study-lie-algebras).