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.

Last revised on August 27, 2018 at 18:38:23. See the history of this page for a list of all contributions to it.