(n-1)-Step Derivations on n-Groupoids: The Case n=3

Abstract

We define a ranked trigroupoid as a natural followup on the idea of a ranked bigroupoid. We consider the idea of a derivation on such a trigroupoid as representing a two-step process on a pair of ranked bigroupoids where the mapping d is a self-derivation at each step. Following up on this idea we obtain several results and conclusions of interest. We also discuss the notion of a couplet (D, d) on X, consisting of a two-step derivation d and its square D = d circle d, for example, whose defining property leads to further observations on the underlying ranked trigroupoids also.