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Trace- and pseudo-products: restriction-like semigroups with a band of projections

FitzGerald, DG and Kinyon, MK 2021 , 'Trace- and pseudo-products: restriction-like semigroups with a band of projections' , Semigroup Forum, vol. 103, no. 3 , pp. 848-866 , doi: 10.1007/s00233-021-10221-x.

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Abstract

We ascertain conditions and structures on categories and semigroups which admit the construction of pseudo-products and trace products respectively, making their connection as precise as possible. This topic is modelled on the ESN Theorem and its generalisation to ample semigroups. Unlike some other variants of ESN, it is self-dual (two-sided), and the condition of commuting projections is relaxed. The condition that projections form a band (are closed under multiplication) is shown to be a very natural one. One-sided reducts are considered, and compared to (generalised) D-semigroups. Finally the special case when the category is a groupoid is examined.

Item Type: Article
Authors/Creators:FitzGerald, DG and Kinyon, MK
Keywords: ESN theorem, Ehresmann semigroup, restriction semigroup
Journal or Publication Title: Semigroup Forum
Publisher: Springer-Verlag
ISSN: 0037-1912
DOI / ID Number: 10.1007/s00233-021-10221-x
Copyright Information:

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021

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