Isomorphism extension properties in normal categories and normal duals
Akhila Rajan, Namitha Sara Mathew, Bingjun Yu · Asian-European Journal of Mathematics · 2022
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].