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Wreath products involving symmetric inverse monoids/semigroups/categoriesarise in many areas of algebra and science, and presentations by generators andrelations are crucial tools in such studies. The current paper finds suchpresentations for $M\wr\mathcal I_n$, $M\wr\operatorname{Sing}(\mathcal I_n)$and $M\wr\mathcal I$. Here $M$ is an arbitrary monoid, $\mathcal I_n$ is thesymmetric inverse monoid, $\operatorname{Sing}(\mathcal I_n)$ its singularideal, and $\mathcal I$ is the symmetric inverse category.

Presentations for wreath products involving symmetric inverse monoids and categories