[[!redirects Preord]] [[!redirects Prost]] $PreOrd$ denotes the category of [[preordered sets]] and order-preserving maps. The category $PreOrd$ is [[topological functor|topological]] over $Set$ and therefore enjoys strong completeness and cocompleteness properties; see [[total category]]. It is also a [[locally presentable category]]. $PreOrd$ is a [[cartesian closed category]]. In fact it is an [[exponential ideal]] in the cartesian closed category [[Cat]].