An ordered framework for partial multivalued functors

The category Rel of sets and relations intimately ties the notions of function, partial multivalued function, and direct image under a function through the description of Rel as the Kleisli category of the covariant power set functor on Set. We present a suitable framework to obtain a similar relationship between the concepts of functor, partial multivalued functor, and the direct image under a functor.Comment: Accepted for presentation at the Asia-Pacific World Congress on Computer Science and Engineering 2015, Fij