Certain Properties of $K_0$-monoids Preserved by Tracial Approximation We show that the following $K_0$-monoid properties of $C^*$-algebras in the class $\Omega$ are inherited by simple unital $C^*$-algebras in the class $TA\Omega$: (1) weak comparability, (2) strictly unperforated, (3) strictly cancellative. Keywords:$C^*$-algebra, tracial approximation, $K_0$-monoidCategories:46L05, 46L80, 46L35