We show Exel’s tight representation of an inverse semigroup can be described in terms of joins and covers in the natural partial order. Using this, we show that the ${C}^{\ast } $ -algebra of a finitely aligned category of paths, developed by Spielberg, is the tight ${C}^{\ast } $ -algebra of a natural inverse semigroup. This includes as a special case finitely aligned higher-rank graphs: that is, for such a higher-rank graph $\Lambda $ , the tight ${C}^{\ast } $ -algebra of the inverse semigroup associated to $\Lambda $ is the same as the ${C}^{\ast } $ -algebra of $\Lambda $ .