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?.

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?.

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 thread mathoverflow.net/questions/58696/why-study-lie-algebras .

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?.