The concept of a binary relation over partial enumerated sets (Q1317613)

Binary relations over total enumerated sets have been introduced and investigated in an earlier paper [the author, Z. Math. Logik Grundlagen Math. 34, No. 3, 265-276 (1988; Zbl 0657.03026)]. In the present paper we analyze the possibility of extending this concept of partial enumerated sets. In doing so, we work within the general methodological framework outlined in the introduction to the above-mentioned paper. In the first section, we consider some class of monads called ``lifts of the power set monad''. The monads serve as tools for describing the relations investigated here. In the second section, we discuss possible natural definitions of relations over partial enumerated sets. Together with relations described by Kleisli categories of suitable monads (called ``\(T\)-relations''), we also introduce the so-called ``quasi-relations''. The latter class cannot be described by ``monadic machinery''.