nLab PreOrd

$PreOrd$ denotes the category of preorders and order-preserving maps.

The category $PreOrd$ is 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.

Created on September 21, 2017 at 14:30:53. See the history of this page for a list of all contributions to it.