Some categorical remarks on non-associative algebras

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.