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
