Authors: Krapež, Aleksandar 
Petrić, Zoran 
Title: A note on semisymmetry
Journal: Quasigroups and Related Systems
Volume: 25
Issue: 2
First page: 269
Last page: 278
Issue Date: 1-Jan-2017
ISSN: 1561-2848
J.D.H. Smith showed how to replace homotopies between quasigroups by homo-morphism between semisymmetric quasigroups. This is a semisymmetrization and it replaces a quasigroup by a semisymmetric structure defined on its Cartesian cube. The reason for a semisymmetrization is that homomorphisms behave more regularly than homotopies. A thorough survey of properties of Smith's semisymmetrization is given in this paper. Also, new semisymmetrizations, which replace a quasigroup by semisymmetric structures defined on its Cartesian square are suggested.
Keywords: Adjunction | Category | Embedding | Functor | Homotopy | Monadic adjunction | Quasigroup | Semisymmetrization | Variety
Publisher: Institute of Mathematics, Academy of Sciences Moldova
Project: Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 
Representations of logical structures and formal languages and their application in computing 

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