Sibert, H. 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. Reviewer: V.V.Vershinin (Novosibirsk) MSC: 18D35 Structured objects in a category (MSC2010) Keywords:automorphic object; automorphic set; category; quandle; racks PDFBibTeX XMLCite \textit{H. Sibert}, Sib. Math. J. 41, No. 6, 1436--1450 (2000; Zbl 0969.18009); translation from Sib. Mat. Zh. 41, No. 6, 1436--1450 (2000) Full Text: DOI EuDML