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Automorphic objects in categories. (English, Russian) Zbl 0969.18009

Sib. Math. J. 41, No. 6, 1188-1199 (2000); translation from Sib. Mat. Zh. 41, No. 6, 1436-1450 (2000).
The author introduces and studies automorphic objects in categories. There are analogs of group objects with a group replaced by an automorphic set in the sense of E. Brieskorn. The latter is a set with a product for which left translations are automorphisms.
In particular, the author proves the following theorem: In a category \({\mathcal C}\) with finite products, an object \(c\) is automorphic if and only if the \(\operatorname{hom}\) functor \({\mathcal C}(-,c)\) is an automorphic object in the functor category \({\mathcal S}et^{{\mathcal C}^{op}}\).
In the last section, the author presents various examples of automorphic objects, connected with racks and quandles arising in low-dimensional topology.

MSC:

18D35 Structured objects in a category (MSC2010)
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