Properly posed, Vasili's question should be not

Given that poset adjoints are considered miniature versions of adjoints, what are are the unit and co-unit natural transformations say between poset A and B?

but: : Given order-preserving functions r: A --> B and l: B --> A between : posets A and B, with r right adjoint to l, what are the unit and : co-unit natural transformations 1_B ==> rl and lr ==> 1_A ? And the answer, as always, is that 1_B: b --> rlb (for b in B) is the order relation b < rlb that adjointness correlates to lb < lb, while 1_A: lra --> a (for a in A) is the order relation lra < a that adjointness correlates to ra < ra. (Above I'm writing simply < for the (reflexive, transitive) order relation on either of the two posets.) HTH. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]