We show that quandle coverings in the sense of Eisermann form a (regular epi)-reflective subcategory of the category of surjective quandle homomorphisms, both by using arguments coming from categorical Galois theory and by constructing concretely a centralization congruence. Moreover, we show that a similar result holds for normal quandle extensions.
How to centralize and normalize quandle extensions / M. Duckerts-Antoine, V. Even, A. Montoli. - In: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. - ISSN 0218-2165. - 27:2(2018 Feb). [10.1142/S0218216518500207]
How to centralize and normalize quandle extensions
A. Montoli
Ultimo
2018
Abstract
We show that quandle coverings in the sense of Eisermann form a (regular epi)-reflective subcategory of the category of surjective quandle homomorphisms, both by using arguments coming from categorical Galois theory and by constructing concretely a centralization congruence. Moreover, we show that a similar result holds for normal quandle extensions.
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