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On categories of structures and classes of algebras

J. Jeżek — 1970

CONTENTS1. Introduction and preliminaries.............................................................................. 52. Pre-scategories and scategories......................................................................... 63. Scategorization......................................................................................................... 84. Abstract scategories................................................................................................ 95. Substructures and products...

Quasigroup covers of division groupoids

Jaroslav J. Ježek;  Tomáš Kepka;  Petr Němec — 2023

Commentationes Mathematicae Universitatis Carolinae

Let G be a division groupoid that is not a quasigroup. For each regular cardinal α > | G | we construct a quasigroup Q on G × α that is a quasigroup cover of G (i.e., G is a homomorphic image of Q and G is not an image of any quasigroup that is a proper factor of Q ). We also show how to easily obtain quasigroup covers from free quasigroups.

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