IDEMPOTENT AND DISTRIBUTIVE GROUP RELATED GROUPOIDS, II
Norbert Endres · Demonstratio Mathematica · 1996
In the final chapter we deal with the transfer of algebraic identities and the property of being a SGii/£)-groupoid from a groupoid (TZ,*) to its derived groupoids, i.e. to groupoids with the same underlying set and a binary operation, which is made up of iterated applications of • and the trivial binary operations on TZ.In particular, we turn our attention to the ¿-symmetry law and describe SGRID-groupoids satisfying this identity.For describing mappings or homomorphisms of 5G !.ft/-groupoids,depending on the situation we sometimes only need their counterparts restricted in domain, or range, or domain and range, respectively (see also text after ([E4],(1.5))).Since what is meant always comes clear from the context, and since we don't want to exaggerate with precision in notation, which would make a mess of the formulation of some results, for a mapping and corresponding restrictions we use the same symbol.