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A monoid $S$ is right coherent if every finitely generated subact of everyfinitely presented right $S$-act itself has a finite presentation; it is weaklyright coherent if every finitely generated right ideal of $S$ has a finitepresentation. We show that full and partial transformation monoids, symmetricinverse monoids and partition monoids over an infinite set are all weakly rightcoherent, but that none of them is right coherent. Left coherency and weak leftcoherency are defined dually, and the corresponding results hold for theseproperties. In order to prove the non-coherency results, we give a presentationof an inverse semigroup which does not embed into any left or right coherentmonoid.

Coherency properties for monoids of transformations and partitions