Homotopy and semisymmetry of quasigroups
type: Item
instance of: scholarly article
title: Homotopy and semisymmetry of quasigroups
zbMATH Open document ID: 0906.20046
author: J. D. H. Smith
published in: Algebra Universalis
publication date: 1998-11-23T00:00:00Z
review text: A quasigroup \({\mathcal Q}=(Q;\cdot,/,\setminus)\) is called semisymmetric if it satisfies the identity \((y\cdot x)y=x\); \(\mathcal Q\) is central if the diagonal \(\{(q,q);\;q\in Q\}\) is a normal subquasigroup of \({\mathcal Q}\times{\mathcal Q}\); \(\mathcal Q\) is entropic if it satisfies the identity \((xy)(zt)=(xz)(yt)\). By \(\mathbf{Qtp}\) is denoted the category of all quasigroups with homotopies between them and by \(\mathbf{Ztp}\) the category of central quasigroups with homotopies. Main results: The category \(\mathbf{Qtp}\) is isomorphic to a category of homomorphisms between semisymmetric quasigroups. The category \(\mathbf{Ztp}\) is isomorphic to a category of homomorphisms between entropic semisymmetric quasigroups.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 08C05
zbMATH DE Number: 1226234
zbMATH Keywords: categories of quasigroups
zbMATH Keywords: homotopies
zbMATH Keywords: central quasigroups
zbMATH Keywords: semisymmetric quasigroups
zbMATH Keywords: entropic quasigroups
zbMATH Keywords: identities
MaRDI profile type: Publication
full work available at URL: s000120050046
OpenAlex ID: W2007880116
DOI: 10.1007/S000120050046
description: scientific article; zbMATH DE number 1226234