2025/07/07 by Luka Carroll, James E. East, Carroll, Luka +3
Computer Science · Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2507.05497
openalex publication_date 2025/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The full-domain partition monoid Pnfd has been discovered independently in two recent studies on connections between diagram monoids and category theory. It is a right restriction Ehresmann monoid, and contains both the full transformation monoid and the join semilattice of equivalence relations. In this paper we give presentations (by generators and relations) for Pnfd, its singular ideal, and its planar submonoid. The latter is not an Ehresmann submonoid, but it is a so-called grrac monoid in the terminology of Branco, Gomes and Gould. In particular, its structure is determined in part by a right regular band in one-one correspondence with planar equivalences.