nLab
opposite poset

Given a poset (or proset) $P$, its opposite (or dual, inverse, converse, reverse, etc), denoted $P^{op}$ (among other ways), is the poset (or proset) with the same underlying set, with $x \leq y$ in $P^op$ iff $y \leq x$ (equivalently, $x \geq y$) in the original $P$. This is a special case of both an opposite relation and an opposite category.