Abstract
Structure theory of regular semigroups has been using theory of categories to a great extent. Structure theory of regular semigroups developed by K.S.S. Nambooripad using inductive groupoids, structure of combinatorial regular semigroups developed by A.R. Rajan and several other structure theories have made extensive use of categories. The theory of cross connections developed by K.S.S. Nambooripad has provided an abstract description of the category of left ideals of a regular semigroup which he called normal category. The first appearance of categories in structure theory can be traced to Schein’s structure theory of inverse semigroups which uses groupoids as a basic object where groupoids are categories in which all morphisms are isomorphisms. Schein described the category of isomorphisms between order ideals of the set of idempotents of an inverse semigroup and called them inductive groupoids. Some instances of appearance of categories in structure theory of certain classes of regular semigroups are presented here.
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The author thanks the Kerala State Council for Science Technology and Environment (KSCSTE) for the support under Emeritus Scientist Scheme which facilitated the participation in the conference.
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Rajan, A.R. (2016). Structure Theory of Regular Semigroups Using Categories. In: Rizvi, S., Ali, A., Filippis, V. (eds) Algebra and its Applications. Springer Proceedings in Mathematics & Statistics, vol 174. Springer, Singapore. https://doi.org/10.1007/978-981-10-1651-6_14
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DOI: https://doi.org/10.1007/978-981-10-1651-6_14
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