Isomorphism extension properties in normal categories and normal duals

Author:

Rajan A. R.1,Mathew Namitha Sara2,Yu Bingjun3

Affiliation:

1. Institute of Mathematics Research and Training (IMRT) and, Department of Mathematics, University of Kerala, Thiruvananthapuram 695581, India

2. Department of Mathematics, St. Joseph’s College for Women, Alappuzha 688001, India

3. College of Mathematical Science, Sichuan Normal University, Chengdu 610066, P. R. China

Abstract

The normal categories associated with unit regular semigroups and various classes of strongly unit regular semigroups were described as [Formula: see text]-categories with appropriate isomorphism extension properties. The normal categories associated with unit regular semigroups have been characterized as weak [Formula: see text]-categories. The cases of [Formula: see text]-strongly unit regular, [Formula: see text]-strongly unit regular and strongly unit regular semigroups were characterized using corresponding forms of isomorphism extensions. It is shown that when a normal category satisfies one of these isomorphism extension properties, then its normal dual satisfies a corresponding isomorphism extension property. Further, we give a description of the extension isomorphisms in the dual [Formula: see text] in terms of extensions in [Formula: see text].

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

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