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On factorization systems for surjective quandle homomorphisms

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Even, Valérian [UCL] Gran, Marino [UCL]

We study and compare two factorization systems for surjective homomorphisms in the category of quandles. The first one is induced by the adjunction between quandles and trivial quandles, and a precise description of the two classes of morphisms of this factorization system is given. In doing this we observe that a special class of congruences in the category of quandles always permute in the sense of the composition of relations, a fact that opens the way to some new universal algebraic investigations in the category of quandles. The second factorization system is the one discovered by E. Bunch, P. Lofgren, A. Rapp and D. N. Yetter. We conclude with an example showing a difference between these factorization systems.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2014
Language Anglais
Journal information "Journal of Knot Theory and Its Ramifications" - Vol. 23, no. 11 (2014)
Peer reviewed yes
Publisher World Scientific Publishing Co. Pte. Ltd. ((Singapore) Singapore)
issn 0218-2165
e-issn 1793-6527
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Keywords Quandle ; factorisation system ; permutability of congruences.
Links
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Bibliographic reference Even, Valérian ; Gran, Marino. On factorization systems for surjective quandle homomorphisms. In: Journal of Knot Theory and Its Ramifications, Vol. 23, no. 11 (2014)
Permanent URL http://hdl.handle.net/2078.1/152097