Geodesic
On alternating semigroups of endomorphisms of a groupoid
Matematičeskie trudy, Tome 27 (2024) no. 1, pp. 73-95 Cet article a éte moissonné depuis la source Math-Net.Ru

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The bipolar types of composition of a pair of endomorphisms of a groupoid are studied in this work. The notion of an alternating pair of endomorphisms of a groupoid is introduced. For such pairs, a formula is established for calculating the bipolar type of a composition using the bipolar types of endomorphisms included in the composition. Alternating and special alternating semigroups of endomorphisms of a groupoid are introduced. Any two endomorphisms from an alternating endomorphism semigroup form an alternating pair. It is shown that the basic set of endomorphisms of the first type is a special alternating semigroup with identity (that is, a monoid). We study the connection between special alternating endomorphism semigroups of two isomorphic groupoids $G$ and $G'$. It is established that every special alternating semigroup of endomorphisms of the groupoid $G$ is isomorphic to some special alternating semigroup of the groupoid $G'$. 
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A. V. Litavrin. On alternating semigroups of endomorphisms of a groupoid. Matematičeskie trudy, Tome 27 (2024) no. 1, pp. 73-95. http://geodesic.mathdoc.fr/item/MT_2024_27_1_a1/

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