2023/12/28 by Nóra Szakács, Szakács, Nóra · 1 citation
Arts and Humanities · Computer Science · Mathematics · #Linguistics and Discourse Analysis #semigroups and automata theory #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2312.16976
We show that the category of X-generated E-unitary inverse monoids with greatest group image G is equivalent to the category of G-invariant, finitary closure operators on the set of connected subgraphs of the Cayley graph of G. Analogously, we study F-inverse monoids in the extended signature (⋅, 1, -1, ^\mathfrakm), and show that the category of X-generated F-inverse monoids with greatest group image G is equivalent to the category of G-invariant, finitary closure operators on the set of all subgraphs of the Cayley graph of G. As an application, we show that presentations of F-inverse monoids in the extended signature can be studied by tools analogous to Stephen's procedure in inverse monoids, in particular, we introduce the notions of F-Schützenberger graphs and P-expansions.