2019/11/30 by P. A. Azeef Muhammed, Mikhail V. Volkov, Muhammed, P. A. Azeef +3
Computer Science · Decision Sciences · #18B40 #20M10 #20M17 #20M18 #20M50 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1912.00214
openalex publication_date 2019/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Locally inverse semigroups are regular semigroups whose idempotents form pseudo-semilattices. We characterise the categories that correspond to locally inverse semigroups in the realm of Nambooripad's cross-connection theory. Further, we specialise our cross-connection description of locally inverse semigroups to inverse semigroups and completely 0-simple semigroups, obtaining structure theorems for these classes. In particular, we show that the structure theorem for inverse semigroups can be obtained using only one category, quite analogous to the Ehresmann-Schein-Nambooripad Theorem; for completely 0-simple semigroups, we show that cross-connections coincide with structure matrices, thus recovering the Rees Theorem by categorical tools.