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 | Abstract: | 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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