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Cross-sections of Green’s relations in a symmetric inverse 0-category. (English. Russian original) Zbl 1264.20075

Algebra Logic 51, No. 4, 306-318 (2012); translation from Algebra Logika 51, No. 4, 458-475 (2012).
Given a non-empty set \(X\) consider the category whose objects are subsets of \(X\) and morphisms are all bijective maps between these subsets. In the paper under review the author considers the semigroup of morphisms of this category (morphisms which are not composable in the category compose to the zero element in the semigroup). For this semigroup the author classifies cross-sections of all Green’s relations, describes these cross-sections up to isomorphism and also counts their number in the case when \(X\) is a finite set.

MSC:

20M50 Connections of semigroups with homological algebra and category theory
20M20 Semigroups of transformations, relations, partitions, etc.
20M18 Inverse semigroups
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