Lie algebra and category theory

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This winter I have back to back an exam on introductory category theory (very basic, the biggest thing we did is the connection between (co-)products and adjoints) and an exam on Lie Algebras (up to classification, with no mention of Lie groups). Given that they are back to back I was wondering if anybody knew of fun exercises to practice both at the same time. A pdf or a particular exercise you have done, both work fine. Thanks a lot in advance. (something like finding the adjoint(s) if there are any to the forgetful functor from lie algebras to vector spaces)