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ON PSEUDO-EHRESMANN SEMIGROUPS

Part of: Semigroups

Published online by Cambridge University Press:  18 June 2018

SHOUFENG WANG
SHOUFENG WANG*
Affiliation:
Department of Mathematics, Yunnan Normal University, Kunming, Yunnan, 650500, PR China email wsf1004@163.com
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Abstract

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As generalizations of inverse semigroups, Ehresmann semigroups are introduced by Lawson and investigated by many authors extensively in the literature. In particular, Lawson has proved that the category of Ehresmann semigroups and admissible morphisms is isomorphic to the category of Ehresmann categories and strongly ordered functors, which generalizes the well-known Ehresmann–Schein–Nambooripad (ESN) theorem for inverse semigroups. From a varietal perspective, Ehresmann semigroups are derived from reducts of inverse semigroups. In this paper, inspired by the approach of Jones [‘A common framework for restriction semigroups and regular $\ast$-semigroups’, J. Pure Appl. Algebra216 (2012), 618–632], Ehresmann semigroups are extended from a varietal perspective to pseudo-Ehresmann semigroups derived instead from reducts of regular semigroups with a multiplicative inverse transversal. Furthermore, motivated by the method used by Gould and Wang [‘Beyond orthodox semigroups’, J. Algebra368 (2012), 209–230], we introduce the notion of inductive pseudocategories over admissible quadruples by which pseudo-Ehresmann semigroups are described. More precisely, we show that the category of pseudo-Ehresmann semigroups and (2,1,1,1)-morphisms is isomorphic to the category of inductive pseudocategories over admissible quadruples and pseudofunctors. Our work not only generalizes the result of Lawson for Ehresmann semigroups but also produces a new approach to characterize regular semigroups with a multiplicative inverse transversal.

Keywords

pseudo-Ehresmann semigroupinductive pseudocategoryadmissible quadrupleEhresmann semigroupmultiplicative inverse transversal

MSC classification

Primary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 105 , Issue 2 , October 2018 , pp. 257 - 288
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The author is supported by the National Natural Science Foundations of China (11661082,11301470).

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