# Normal categories of semigroup of order-preserving transformations on a finite chain

Source: [Normal categories of semigroup of order-preserving transformations on a finite chain](<https://www.sota2.com/research/paper/68fa59e71e209131ce9bb438>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T05:25:34.752Z

Authors: K K Sneha, P G Romeo

Published: 2022-12-11T09:14:00.000Z

## Abstract

K. S. S. Nambooripad intoduced nornal categories to enable to describe the structure of regular semigroups fully. In this paper we describe the ideal categories of the regular semigroup $OX\_n,$ of non-invertible order-preserving transformations on a finite chain $X\_n=\\{1\\leq 2\\leq \\cdots \\leq n \\}$ which are normal categories. Further it is shown that the principal left ideal category of $OX\_n$ as the power set category $P\_o(X\_n)$ of $OX\_n$ and the principal right ideal category as $\\prod\_o(X\_n)$ category of ordered partitions of $X\_n$ and described the cone semigroup $T\\mathscr L(OX\_n)$ and prove that it is isomorphic to $OX\_n.$

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2212.05453>)

[PDF](<https://arxiv.org/pdf/2212.05453.pdf>)