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arXiv · 2608.24657

Free left $h$-Ehresmann semigroups

Daniel Heath
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Abstract

The class of left $h$-adequate semigroups sits between the classes of left ample and left Ehresmann semigroups. Whilst free objects in related classes have descriptions in terms of directed trees, free left $h$-adequate semigroups have yet only been described in terms of Rees quotients of free products. Here, we reintroduce the class of (left) $h$-Ehresmann semigroups, show their free objects coincide with free (left) $h$-adequate semigroups, and give a description of these free objects in terms of directed trees. We use our new description in investigating various properties of these structures, including finitary conditions of recent interest.

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Daniel Heath. 2026-08-25. Free left $h$-Ehresmann semigroups. https://arxiv.org/abs/2608.24657

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