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Inductive and projective limits of covering \(k\)-groups of \(n\)-groups. (English) Zbl 0568.20062

The paper is a continuation of the description of the category \(Cov^ k_ n\) of covering \(k\)-groups of \(n\)-groups [see the author, Bull. Acad. Pol. Sci., Ser. Sci. Math. 27, 437-441 (1979; Zbl 0424.18003) and Demonstr. Math. 16, 977-990 (1983; Zbl 0556.20051)]. The author gives constructions of inductive and projective limits in \(Cov^ k_ n\) and defines a pair of adjoint functors \(\Gamma\) and \(\Lambda\) as well. Based on properties of these functors the author shows that the category \(Gr_{n+1}\) of \((n+1)\)-groups is a full reflective subcategory of \(Cov^{k+1}_{n+1}\) (where \(n=sk\)).
Reviewer: B.Gleichgewicht

MSC:

20N15 \(n\)-ary systems \((n\ge 3)\)
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
20M50 Connections of semigroups with homological algebra and category theory
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
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