Dear all, It is well-known that there exists an adjunction between the category of Lie algebras and the category of Hopf algebras, by taking the universal algebra of a lie algebra, and the primitive elements of a Hopf algebra. Both the notion of a Hopf algebra and a Lie algebra make sense in the setting of an additive symmetric monoidal category. Is it possible to preform the above mentioned adjunction in this general setting, probably assuming extra conditions on the monoidal category one is working in, such as the existence of certain (co)limits and preservation of these (co)limits by the tensor product ? Does anyone know a reference for such a result ? Many thanks and best wishes, Joost Vercruysse. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]