Natural transformations for quasigroupoids. (English) Zbl 1520.20127
Summary: In this paper, we introduce the notions of natural transformation between morphisms of quasigroupoids and between morphisms of weak Hopf quasigroups. Also, we prove that natural transformations between morphisms of finite quasigroupoids come from natural transformations between morphisms of weak Hopf quasigroups and, on the other hand, we obtain that every natural transformation for morphisms defined between pointed cosemisimple weak Hopf quasigroups comes from a natural transformation between finite quasigroupoids.
Keywords:
quasigroup; quasigroupoid; groupoid; Hopf quasigroup; weak Hopf quasigroup; weak Hopf algebra; morphism of quasigroupoids; natural transformationReferences:
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