# On inverse categories with split idempotents

## Emil Schwab and Emil Daniel Schwab

Address:

Department of Mathematical Sciences, West University of Timisoara, Timisoara, Romania

Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas 79968, USA

E-mail:

schwab@math.uvt.ro

eschwab@utep.edu

Abstract: We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents which generate (right or left) principal ideals of annihilators.

AMSclassification: primary 20M50; secondary 18B40.

Keywords: inverse categories, inverse monoids, split idempotents, pointed sets, annihilators, exact sequences.

DOI: 10.5817/AM2015-1-13