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K. S. S. Nambooripad intoduced nornal categories to enable to describe thestructure of regular semigroups fully. In this paper we describe the idealcategories of the regular semigroup $OX_n,$ of non-invertible order-preservingtransformations on a finite chain $X_n=\{1\leq 2\leq \cdots \leq n \}$ whichare normal categories. Further it is shown that the principal left idealcategory of $OX_n$ as the power set category $P_o(X_n)$ of $OX_n$ and theprincipal right ideal category as $\prod_o(X_n)$ category of ordered partitionsof $X_n$ and described the cone semigroup $T\mathscr L(OX_n)$ and prove that itis isomorphic to $OX_n.$

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