2-category algebras?

We all know about group algebras, and this leads naturally to the idea of a category algebra: form a vector space having as a basis the morphisms in a given category, with the obvious product (taking the product of two morphisms to be zero if the head of one isn't the tail of the other). I used an example of this in my paper "Quantum Gravity and the Algebra of Tangles," but I have never seen a reference to the general concept, and I would appreciate one. What I am now interested in, however, is generalizing this notion to 2-category algebras. This might be related to recent algebraic work of Ruth Lawrence, which I haven't actually seen. Any leads? Regards, John Baez