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Extending the Ehresmann-Schein-Nambooripad Theorem

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Abstract

We extend the ‘∨-premorphisms’ part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive categories, following on from a result of Lawson (J. Algebra 141:422–462, 1991) for the ‘morphisms’ part. However, it is so-called ‘∧-premorphisms’ which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type theorem for (ordered) ∧-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem in the inverse case.

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Author notes

  1. Christopher Hollings

    Present address: Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford, OX1 3LB, UK

Authors and Affiliations

  1. Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    Christopher Hollings

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  1. Christopher Hollings
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Correspondence to Christopher Hollings.

Additional information

Communicated by Steve Pride.

This work was completed as part of Project POCTI/0143/2007 of CAUL, financed by FCT and FEDER, and also as part of FCT post-doctoral research grant SFRH/BPD/34698/2007. Thanks must go to both Mark Lawson and Victoria Gould for a number of useful comments.

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Hollings, C. Extending the Ehresmann-Schein-Nambooripad Theorem. Semigroup Forum 80, 453–476 (2010). https://doi.org/10.1007/s00233-010-9215-4

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  • DOI: https://doi.org/10.1007/s00233-010-9215-4

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