An Ehresmann-Schein-Nambooripad-Type Theorem for a Class of P-Restriction Semigroups

作者：Wang, Shoufeng^*

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42(2): 535-568.

DOI：10.1007/s40840-017-0497-5

• Locally restriction P-restriction semigroup
• Inductive generalized category over a local semilattice
• Projection algebra
• ESN-type theorem

As generalizations of inverse semigroups, restriction semigroups and regular -semigroups are investigated by many authors extensively in the literature. In particular, Lawson and Hollings have proved that the category of restriction semigroups together with prehomomorphisms (resp. (2,1,1)-homomorphisms) is isomorphic to the category of inductive categories together with ordered functors (resp. strongly ordered functors), which generalizes the well-known Ehresmann-Schein-Nambooripad theorem (ESN theorem for short) for inverse semigroups. On the other hand, Imaoka and Fujiwara have also obtained an ESN-type theorem for locally inverse regular -semigroups. Recently, Jones generalized restriction semigroups and regular -semigroups to P-restriction semigroups from a varietal perspective and considered the constructions of P-restriction semigroups by using Munn's approach. In this paper, we shall study the class of P-restriction semigroups by using category approach. We introduce the notion of inductive generalized categories over local semilattices by which a class of P-restriction semigroups called locally restriction P-restriction semigroups is described. Moreover, we show that the category of locally restriction P-restriction semigroups together with (2,1,1)-prehomomorphisms (resp. (2,1,1)-homomorphisms) is isomorphic to the category of inductive generalized categories over local semilattices together with preadmissible mappings (resp. admissible mappings). Our work may be regarded as extending the ESN-type theorems for restriction semigroups and locally inverse regular -semigroups, respectively.

• 出版日期2019-3
• 单位云南师范大学