Abstract
E. Bunch, P. Lofgren, A. Rapp and D. N. Yetter [4] pointed out that by considering inner automorphism groups of quandles, one has a functor from the category of quandles with surjective homomorphisms to that of groups with surjective homomorphisms. In this paper, we focus on faithful quandles. As main results, we give a category equivalence between the category of faithful quandles with surjective quandle homomorphisms and that of pairs of groups and their conjugation-stable generators with suitable group homomorphisms. We are also interested in injective quandle homomorphisms. By defining suitable morphisms among pairs of groups and their conjugation-stable generators, we obtain a category which is equivalent to the category of faithful quandles with injective quandle homomorphisms.
Acknowledgement
The author would like to thank Hiroshi Tamaru, Takayuki Okuda and Akira Kubo for valuable advices and encouragements.
Citation
Yasuki Tada. "On categories of faithful quandles with surjective or injective quandle homomorphisms." Hiroshima Math. J. 54 (1) 61 - 86, March 2024. https://doi.org/10.32917/h2022017
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