ON CONDITIONS FOR CONSTELLATIONS

Abstract

A constellation is a set with a partially-defined binary operation and a unary operation satisfying certain conditions, which, loosely speaking, provides a ‘one-sided’ analogue of a category, where we have a notion of ‘domain’ but not of ‘range’. Upon the introduction of an ordering, we may define so-called inductive constellations. These prove to be a significant tool in the study of an important class of semigroups, termed left restriction semigroups, which arise from the study of systems of partial transformations. In this paper, we study the defining conditions for (inductive) constellations and determine that certain of the original conditions from previous papers are redundant. Having weeded out this redundancy, we show, by the construction of suitable counterexamples, that the remaining conditions are independent.

Keywords

• constellation, replete, right cancellative, ordered, inductive

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