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CONTENTS1. Introduction and preliminaries.............................................................................. 52. Pre-scategories and scategories......................................................................... 63. Scategorization......................................................................................................... 84. Abstract scategories................................................................................................ 95. Substructures and products...
Let be a division groupoid that is not a quasigroup. For each regular cardinal we construct a quasigroup on that is a quasigroup cover of (i.e., is a homomorphic image of and is not an image of any quasigroup that is a proper factor of ). We also show how to easily obtain quasigroup covers from free quasigroups.
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