From the point of view of category theory, varieties of non-associative algebras are exceptionally well behaved; formally simple, yet structurally rich, they are an excellent source of examples and counterexamples. Questions in the context of categorical algebra have recently led to some new results on non-associative algebras. In this talk, we explain how we obtained new category-theoretical characterizations of the varieties of associative algebras and of Lie algebras over an infinite field, with an emphasis on our motivation and an overview of the methods we used.
Linden et al. (Wed,) studied this question.