Happy New Year, everyone. I have been wondering about a little question. Category theory texts talk about "algebras" for an endofunctor, which are arrows of type FA -> A, and dually coalgebras A -> GA. I am interested in the symmetric case, arrows of type FA -> GA for endofunctors F and G. Have such structures been studied? This is only scratching the surface. One can ask for a family of such arrows for an algebra. One can consider functors F,G: C -> D between different categories leading to algebras of the form <A, f:FA->GA> where A is an object of C, and f an arrow in D, and so on. I am also interested in the "diagonal" case, arrows of type FAA -> GAA where F and G are functors C^op x C -> C. (Note that all these structures have a "natural" notion of homomorphisms.) I would appreciate any pointers to the literature. Uday Reddy