Presentations for wreath products involving symmetric inverse monoids and categories

Wreath products involving symmetric inverse monoids/semigroups/categories arise in many areas of algebra and science, and presentations by generators and relations are crucial tools in such studies. The current paper finds such presentations for M≀In, M≀Sing(In) and M≀I. Here M is an arbitrary monoid, In is the symmetric inverse monoid, Sing(In) its singular ideal, and I is the symmetric inverse category.