  We study algebras defined by identities in symmetric monoidal categories. Our
focus is on Lie algebras. Besides usual Lie algebras, there are examples
appearing in the study of knot invariants and Rozansky-Witten invariants. Our
main result is a proof of Westbury's conjecture for K3-surface: there exists a
Lie algebra homomorphism from Vogel's universal simple Lie algebra to the Lie
algebra describing the Rozansky-Witten invariants of a K3-surface. Most of the
paper involves setting up a proper language to discuss the problem and we
formulate nine open questions as we proceed.
