Preordered class

In mathematics, a preordered class is a class equipped with a preorder.

Then, it is convenient to use the language of relations on a set.

Partially ordered class and totally ordered class are defined in a similar way.

However, it is difficult to work with them as in the small case because many constructions common in a set theory are no longer possible in this framework.

Equivalently, a preordered class is a thin category, that is, a category with at most one morphism from an object to another.