Hi everybody, I have the following situation. Let C and D be (small) categories, and let T : C x D ---> C x D be a monad, `x' denoting the product on Cat. Using the universal property of the product, T regarded as a *functor* can be decomposed into two *functors* T1 : C x D ---> C and T2 : C x D ---> D such that their pairing <T1,T2> is equal to T. Now my question: in the above situation, is it possible to ensure that T is a monad *only in terms of conditions on T1 and T2*? A trivial example is the pairing of the two projections themselves, which gives the identity functor/monad, just a coincidence? Cheers, Marco -- Marco Kick mailto:M.Kick@sms.ed.ac.uk LFCS, University of Edinburgh http://www.dcs.ed.ac.uk/~mk