Abstract
We formulate an alternative approach to describing Ehresmann semigroups by means of left and right étale actions of a meet semilattice on a category. We also characterize the Ehresmann semigroups that arise as the set of all subsets of a finite category. As applications, we prove that every restriction semigroup can be nicely embedded into a restriction semigroup constructed from a category, and we describe when a restriction semigroup can be nicely embedded into an inverse semigroup.
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Notes
My thanks to the referee for this nice observation.
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Acknowledgements
I would like to thank Prof. V. A. R. Gould of the University of York for her comments on an earlier draft of this paper. I would also like to thank the anonymous referee for their careful reading of the submitted paper and helpful suggestions.
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Communicated by Victoria Gould.
This paper is dedicated to the memory of Peter M. Neumann.
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Lawson, M.V. On Ehresmann semigroups. Semigroup Forum 103, 953–965 (2021). https://doi.org/10.1007/s00233-021-10200-2
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DOI: https://doi.org/10.1007/s00233-021-10200-2