Any left Ehresmann monoid with a proper basis is isomorphic to a subsemigroup Q_ℓ(T,X,Y) of a constructed monoid P_ℓ(T,X).
Lawson, On Ehresmann semigroups,Semigroup Forum103 (2021), 953-965
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Left Ehresmann monoids with a proper basis
Any left Ehresmann monoid with a proper basis is isomorphic to a subsemigroup Q_ℓ(T,X,Y) of a constructed monoid P_ℓ(T,X).