On Ehresmann semigroups

Mark V. Lawson

doi:10.1007/s00233-021-10200-2

On Ehresmann semigroups

Mark V. Lawson^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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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.

Original language	English
Pages (from-to)	953-965
Number of pages	13
Journal	Semigroup Forum
Volume	103
Issue number	3
Early online date	4 Jun 2021
DOIs	https://doi.org/10.1007/s00233-021-10200-2
Publication status	Published - Dec 2021

Keywords

Categories
Ehresmann semigroups
Finite Boolean algebras

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s00233-021-10200-2

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This is a post-peer-review, pre-copyedit version of an article published in Semigroup Forum. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00233-021-10200-2
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abstract = "We formulate an alternative approach to describing Ehresmann semigroups by means of left and right {\'e}tale 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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AB - 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.

KW - Categories

KW - Ehresmann semigroups

KW - Finite Boolean algebras

UR - https://www.scopus.com/pages/publications/85107507213

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ER -

On Ehresmann semigroups

Abstract

Keywords

ASJC Scopus subject areas

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