We give the way of composing different types of relational notions under certain condition, for example, ordinary binary relations, up-closed multirelations, ordinary (possibly non-up-closed) multirela-tions, quantale-valued relations, and probabilistic relations. Our key idea is to represent a relational notion as a generalized predicate transformer based on some truth value in some category and to represent it as a Kleisli arrow for some continuation monad. The way of composing those relational notions is given via identity-on-object faithful functors between different Kleisli categories. We give a necessary and sufficient condition to have such identity-on-object faithful functor.
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