Presentations for wreath products involving symmetric inverse monoids and categories

Wreath products involving symmetric inverse monoids/semi-groups/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 l In, M l Sing(In) and M l I. Here M is an arbitrary monoid, In is the symmetric inverse monoid, Sing(In) its sin-gular ideal, and I is the symmetric inverse category. (c) 2023 Elsevier Inc. All rights reserved.