Division Categories and Inverse Semigroups
Abstract
Abstract division categories were introduced by Leech[6] as a small category C having finite pushouts, all of whose morphisms are epimorphisms, and with a quasi initial object. The concept of the division category was originally introduced to help study semigroup coextensions(see [5]). Möbius categories were introduced by Leroux[8]. They were created as a general program to extend the theory of Möbius functions. In [17] Schwab shows that a reduced standard division category of a combinatorial inverse monoid (with the set of idempotents under natural partial order and locally finite) is a Möbius category. In the last section of Chapter 2 a result of Schwab[19] is detailed using the Leech[6] construction of inverse monoids of fractions.
Subject Area
Mathematics
Recommended Citation
Romero, Efren, "Division Categories and Inverse Semigroups" (2006). ETD Collection for University of Texas, El Paso. AAI1435324.
https://scholarworks.utep.edu/dissertations/AAI1435324